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src/MyLib.hs

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let pageDatas = Tree.foldTree folder tree
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let pagesDir = destination File.</> "pages"
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Dir.createDirectoryIfMissing True pagesDir
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let writePageData pg = B.writeFile (pagesDir File.</> (pg ^. pageContent . hash) ++ ".json") (Json.encode pg)
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let writePageData pg = B.writeFile (pagesDir File.</> (pg ^. pageContent . hash) ++ ".json") (PrettyJson.encodePretty pg)
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Monad.forM_ pageDatas writePageData
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return pageDatas
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{"_pageContent":{"_pageTitle":"University Physics with Modern Physics","_hash":"0af5b76897bd59b64b3d577b459c75a1b5b6b3ca","_attributes":{},"_answers":0},"_parentHash":"2aed5404c83f7a46aa249e0a6328af756b19d513","_childPageContents":[{"_pageTitle":"11. Equilibrium and Elasticity","_hash":"ba45627f4d5702a2d14eaced7927fd3798c60167","_attributes":{},"_answers":0}]}
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"_hash": "ba45627f4d5702a2d14eaced7927fd3798c60167",
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"_pageTitle": "11. Equilibrium and Elasticity"
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}
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],
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"_pageContent": {
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"_answers": 0,
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"_attributes": {},
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"_hash": "0af5b76897bd59b64b3d577b459c75a1b5b6b3ca",
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"_pageTitle": "University Physics with Modern Physics"
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},
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"_parentHash": "2aed5404c83f7a46aa249e0a6328af756b19d513"
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}
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{"_pageContent":{"_pageTitle":"5.1 Continuous Mappings","_hash":"2125c437aaac928d5852224ff00a83f9d9776dda","_attributes":{},"_answers":1},"_parentHash":"6c11e3a31b4b8bd07bdef3f87887ab202a568679","_childPageContents":[{"_pageTitle":"8","_hash":"3e8d61043ed9bdb6b3cd4f197f0203bbdcb13db1","_attributes":{"a.md":{"_time":"2020-10-18T14:48:51+09:00","_attributeFile":{"_content":"I'll refer $`\\mathcal{T}`$ as $`\\mathcal{T}_X`$, $`\\mathcal{T}_1`$ as $`\\mathcal{T}_Y`$, $`\\mathcal{T}_2`$ as $`\\mathcal{T}_A`$, $`\\mathcal{T}_3`$ as $`\\mathcal{T}_B`$.\n\nLet's define $`x \\in X`$ and $`U \\in \\mathcal{T}_Y`$ such that $`f(x) \\in U`$. By definition of continuous mapping, there must exists a $`V`$ such that $`x \\in V \\in \\mathcal{T}_X`$ and $`f(x) \\in fV \\subseteq U`$.\n\nIf for any $`x \\in A`$ and any B-induced open set $`U_B \\in \\mathcal{T}_B`$, which must imply existance of $`U \\in \\mathcal{T}_Y`$, such that $`g(x) \\in U_B`$,\n\n![](IMG_44AF9D4BED6C-1.jpeg)\n\n...there exists an A-induced open set $`V_A`$, which must imply existance of $`V \\in \\mathcal{T}_A`$, such that the image $`gV_A`$ satisfies $`g(x) \\in gV_A \\subseteq U_B`$, then $`g`$ must be continuous. What we have to know is that if the image $`gV_A`$is subset of $`U_B`$, in other words, every $`x \\in V_A`$ will satisfiy $`g(x) \\in U_B`$. Let's proove it.\n\n![](IMG_E7FB922B8E70-1.jpeg)\n\n```math\n\\begin{aligned}\n & x \\in V_A \\\\\n & \\rightarrow x \\in V \\\\\n & \\rightarrow g(x) \\in gV \\\\\n & \\rightarrow g(x) \\in \\text{ some } U & \\text{ since } f \\text{ is continuous} \\\\\n & \\rightarrow g(x) \\in U \\cap B & \\text{ since codomain of } g \\text{ is } B \\\\\n & \\rightarrow g(x) \\in U_B\n\\end{aligned}\n```"}},"q.md":{"_time":"2020-04-12T01:08:01+09:00","_attributeFile":{"_content":"Let $`(X,\\mathcal{T})`$ and $`(Y,\\mathcal{T}_1)`$ be topological spaces and $`f:(X,\\mathcal{T}) \\rightarrow (Y,\\mathcal{T}_1)`$ a continuous mapping. Let $`A`$ be a subset of $`X`$, $`\\mathcal{T}_2`$ the induced topology on $`A`$, $`B = f(A)`$, $`\\mathcal{T}_3`$ the induced topology on $`B`$ and $`g:(A,\\mathcal{T}_2) \\rightarrow (B,\\mathcal{T}_3)`$ the restriction of $`f`$ to $`A`$. Prove that $`g`$ is continuous."}}},"_answers":1}]}
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{
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"_childPageContents": [
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{
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"_answers": 1,
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"_attributes": {
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"a.md": {
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"_attributeFile": {
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"_content": "I'll refer $`\\mathcal{T}`$ as $`\\mathcal{T}_X`$, $`\\mathcal{T}_1`$ as $`\\mathcal{T}_Y`$, $`\\mathcal{T}_2`$ as $`\\mathcal{T}_A`$, $`\\mathcal{T}_3`$ as $`\\mathcal{T}_B`$.\n\nLet's define $`x \\in X`$ and $`U \\in \\mathcal{T}_Y`$ such that $`f(x) \\in U`$. By definition of continuous mapping, there must exists a $`V`$ such that $`x \\in V \\in \\mathcal{T}_X`$ and $`f(x) \\in fV \\subseteq U`$.\n\nIf for any $`x \\in A`$ and any B-induced open set $`U_B \\in \\mathcal{T}_B`$, which must imply existance of $`U \\in \\mathcal{T}_Y`$, such that $`g(x) \\in U_B`$,\n\n![](IMG_44AF9D4BED6C-1.jpeg)\n\n...there exists an A-induced open set $`V_A`$, which must imply existance of $`V \\in \\mathcal{T}_A`$, such that the image $`gV_A`$ satisfies $`g(x) \\in gV_A \\subseteq U_B`$, then $`g`$ must be continuous. What we have to know is that if the image $`gV_A`$is subset of $`U_B`$, in other words, every $`x \\in V_A`$ will satisfiy $`g(x) \\in U_B`$. Let's proove it.\n\n![](IMG_E7FB922B8E70-1.jpeg)\n\n```math\n\\begin{aligned}\n & x \\in V_A \\\\\n & \\rightarrow x \\in V \\\\\n & \\rightarrow g(x) \\in gV \\\\\n & \\rightarrow g(x) \\in \\text{ some } U & \\text{ since } f \\text{ is continuous} \\\\\n & \\rightarrow g(x) \\in U \\cap B & \\text{ since codomain of } g \\text{ is } B \\\\\n & \\rightarrow g(x) \\in U_B\n\\end{aligned}\n```"
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},
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"_time": "2020-10-18T14:48:51+09:00"
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},
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"q.md": {
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"_attributeFile": {
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"_content": "Let $`(X,\\mathcal{T})`$ and $`(Y,\\mathcal{T}_1)`$ be topological spaces and $`f:(X,\\mathcal{T}) \\rightarrow (Y,\\mathcal{T}_1)`$ a continuous mapping. Let $`A`$ be a subset of $`X`$, $`\\mathcal{T}_2`$ the induced topology on $`A`$, $`B = f(A)`$, $`\\mathcal{T}_3`$ the induced topology on $`B`$ and $`g:(A,\\mathcal{T}_2) \\rightarrow (B,\\mathcal{T}_3)`$ the restriction of $`f`$ to $`A`$. Prove that $`g`$ is continuous."
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},
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"_time": "2020-04-12T01:08:01+09:00"
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}
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},
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"_hash": "3e8d61043ed9bdb6b3cd4f197f0203bbdcb13db1",
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"_pageTitle": "8"
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}
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],
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"_pageContent": {
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"_answers": 1,
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"_attributes": {},
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"_hash": "2125c437aaac928d5852224ff00a83f9d9776dda",
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"_pageTitle": "5.1 Continuous Mappings"
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},
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"_parentHash": "6c11e3a31b4b8bd07bdef3f87887ab202a568679"
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}
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{"_pageContent":{"_pageTitle":"books","_hash":"2aed5404c83f7a46aa249e0a6328af756b19d513","_attributes":{"q.md":{"_time":"2022-09-25T22:34:28+09:00","_attributeFile":{"_content":"# DON'T PANIC\n\nAlthough it has many omissions and contains much that is apocryphal, or at least wildly inaccurate, but it scores over the other answers over the internet in few important respects. First, the way it is written is very subjective, and second, it has the words DON'T PANIC inscribed in large friendly letters on its home."}}},"_answers":3},"_parentHash":"da39a3ee5e6b4b0d3255bfef95601890afd80709","_childPageContents":[{"_pageTitle":"University Physics with Modern Physics","_hash":"0af5b76897bd59b64b3d577b459c75a1b5b6b3ca","_attributes":{},"_answers":0},{"_pageTitle":"Topology Without Tears","_hash":"4c1513c92422dc16b3c5f13bd03d34ba0feeb6df","_attributes":{"author.txt":{"_time":"2022-09-25T22:34:28+09:00","_attributeFile":{"_content":"Sidney A. Morris"}}},"_answers":1},{"_pageTitle":"Category Theory For Programmers","_hash":"b614f31d04b3bc2b3d23ee4337475251429e5a9f","_attributes":{"author.txt":{"_time":"2022-09-25T22:34:28+09:00","_attributeFile":{"_content":"Bartosz Milewski"}}},"_answers":2}]}
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"_attributes": {},
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"_hash": "0af5b76897bd59b64b3d577b459c75a1b5b6b3ca",
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"_pageTitle": "University Physics with Modern Physics"
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},
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{
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"_answers": 1,
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"_attributes": {
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"author.txt": {
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"_attributeFile": {
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"_content": "Sidney A. Morris"
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},
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"_time": "2022-09-25T22:34:28+09:00"
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}
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},
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"_hash": "4c1513c92422dc16b3c5f13bd03d34ba0feeb6df",
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"_pageTitle": "Topology Without Tears"
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},
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{
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"_answers": 2,
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"_attributes": {
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"author.txt": {
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"_attributeFile": {
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"_content": "Bartosz Milewski"
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},
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"_time": "2022-09-25T22:34:28+09:00"
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}
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},
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"_hash": "b614f31d04b3bc2b3d23ee4337475251429e5a9f",
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"_pageTitle": "Category Theory For Programmers"
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}
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],
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"_pageContent": {
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"_answers": 3,
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"_attributes": {
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"q.md": {
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"_attributeFile": {
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"_content": "# DON'T PANIC\n\nAlthough it has many omissions and contains much that is apocryphal, or at least wildly inaccurate, but it scores over the other answers over the internet in few important respects. First, the way it is written is very subjective, and second, it has the words DON'T PANIC inscribed in large friendly letters on its home."
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},
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"_time": "2022-09-25T22:34:28+09:00"
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}
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},
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"_hash": "2aed5404c83f7a46aa249e0a6328af756b19d513",
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"_pageTitle": "books"
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},
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"_parentHash": "da39a3ee5e6b4b0d3255bfef95601890afd80709"
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}
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{"_pageContent":{"_pageTitle":"8","_hash":"3e8d61043ed9bdb6b3cd4f197f0203bbdcb13db1","_attributes":{"a.md":{"_time":"2020-10-18T14:48:51+09:00","_attributeFile":{"_content":"I'll refer $`\\mathcal{T}`$ as $`\\mathcal{T}_X`$, $`\\mathcal{T}_1`$ as $`\\mathcal{T}_Y`$, $`\\mathcal{T}_2`$ as $`\\mathcal{T}_A`$, $`\\mathcal{T}_3`$ as $`\\mathcal{T}_B`$.\n\nLet's define $`x \\in X`$ and $`U \\in \\mathcal{T}_Y`$ such that $`f(x) \\in U`$. By definition of continuous mapping, there must exists a $`V`$ such that $`x \\in V \\in \\mathcal{T}_X`$ and $`f(x) \\in fV \\subseteq U`$.\n\nIf for any $`x \\in A`$ and any B-induced open set $`U_B \\in \\mathcal{T}_B`$, which must imply existance of $`U \\in \\mathcal{T}_Y`$, such that $`g(x) \\in U_B`$,\n\n![](IMG_44AF9D4BED6C-1.jpeg)\n\n...there exists an A-induced open set $`V_A`$, which must imply existance of $`V \\in \\mathcal{T}_A`$, such that the image $`gV_A`$ satisfies $`g(x) \\in gV_A \\subseteq U_B`$, then $`g`$ must be continuous. What we have to know is that if the image $`gV_A`$is subset of $`U_B`$, in other words, every $`x \\in V_A`$ will satisfiy $`g(x) \\in U_B`$. Let's proove it.\n\n![](IMG_E7FB922B8E70-1.jpeg)\n\n```math\n\\begin{aligned}\n & x \\in V_A \\\\\n & \\rightarrow x \\in V \\\\\n & \\rightarrow g(x) \\in gV \\\\\n & \\rightarrow g(x) \\in \\text{ some } U & \\text{ since } f \\text{ is continuous} \\\\\n & \\rightarrow g(x) \\in U \\cap B & \\text{ since codomain of } g \\text{ is } B \\\\\n & \\rightarrow g(x) \\in U_B\n\\end{aligned}\n```"}},"q.md":{"_time":"2020-04-12T01:08:01+09:00","_attributeFile":{"_content":"Let $`(X,\\mathcal{T})`$ and $`(Y,\\mathcal{T}_1)`$ be topological spaces and $`f:(X,\\mathcal{T}) \\rightarrow (Y,\\mathcal{T}_1)`$ a continuous mapping. Let $`A`$ be a subset of $`X`$, $`\\mathcal{T}_2`$ the induced topology on $`A`$, $`B = f(A)`$, $`\\mathcal{T}_3`$ the induced topology on $`B`$ and $`g:(A,\\mathcal{T}_2) \\rightarrow (B,\\mathcal{T}_3)`$ the restriction of $`f`$ to $`A`$. Prove that $`g`$ is continuous."}}},"_answers":1},"_parentHash":"2125c437aaac928d5852224ff00a83f9d9776dda","_childPageContents":[]}
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{
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"_childPageContents": [],
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"_pageContent": {
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"_answers": 1,
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"_attributes": {
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"a.md": {
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"_attributeFile": {
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"_content": "I'll refer $`\\mathcal{T}`$ as $`\\mathcal{T}_X`$, $`\\mathcal{T}_1`$ as $`\\mathcal{T}_Y`$, $`\\mathcal{T}_2`$ as $`\\mathcal{T}_A`$, $`\\mathcal{T}_3`$ as $`\\mathcal{T}_B`$.\n\nLet's define $`x \\in X`$ and $`U \\in \\mathcal{T}_Y`$ such that $`f(x) \\in U`$. By definition of continuous mapping, there must exists a $`V`$ such that $`x \\in V \\in \\mathcal{T}_X`$ and $`f(x) \\in fV \\subseteq U`$.\n\nIf for any $`x \\in A`$ and any B-induced open set $`U_B \\in \\mathcal{T}_B`$, which must imply existance of $`U \\in \\mathcal{T}_Y`$, such that $`g(x) \\in U_B`$,\n\n![](IMG_44AF9D4BED6C-1.jpeg)\n\n...there exists an A-induced open set $`V_A`$, which must imply existance of $`V \\in \\mathcal{T}_A`$, such that the image $`gV_A`$ satisfies $`g(x) \\in gV_A \\subseteq U_B`$, then $`g`$ must be continuous. What we have to know is that if the image $`gV_A`$is subset of $`U_B`$, in other words, every $`x \\in V_A`$ will satisfiy $`g(x) \\in U_B`$. Let's proove it.\n\n![](IMG_E7FB922B8E70-1.jpeg)\n\n```math\n\\begin{aligned}\n & x \\in V_A \\\\\n & \\rightarrow x \\in V \\\\\n & \\rightarrow g(x) \\in gV \\\\\n & \\rightarrow g(x) \\in \\text{ some } U & \\text{ since } f \\text{ is continuous} \\\\\n & \\rightarrow g(x) \\in U \\cap B & \\text{ since codomain of } g \\text{ is } B \\\\\n & \\rightarrow g(x) \\in U_B\n\\end{aligned}\n```"
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},
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"_time": "2020-10-18T14:48:51+09:00"
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},
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"q.md": {
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"_attributeFile": {
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"_content": "Let $`(X,\\mathcal{T})`$ and $`(Y,\\mathcal{T}_1)`$ be topological spaces and $`f:(X,\\mathcal{T}) \\rightarrow (Y,\\mathcal{T}_1)`$ a continuous mapping. Let $`A`$ be a subset of $`X`$, $`\\mathcal{T}_2`$ the induced topology on $`A`$, $`B = f(A)`$, $`\\mathcal{T}_3`$ the induced topology on $`B`$ and $`g:(A,\\mathcal{T}_2) \\rightarrow (B,\\mathcal{T}_3)`$ the restriction of $`f`$ to $`A`$. Prove that $`g`$ is continuous."
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},
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"_time": "2020-04-12T01:08:01+09:00"
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}
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},
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"_hash": "3e8d61043ed9bdb6b3cd4f197f0203bbdcb13db1",
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"_pageTitle": "8"
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},
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"_parentHash": "2125c437aaac928d5852224ff00a83f9d9776dda"
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}
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{"_pageContent":{"_pageTitle":"Topology Without Tears","_hash":"4c1513c92422dc16b3c5f13bd03d34ba0feeb6df","_attributes":{"author.txt":{"_time":"2022-09-25T22:34:28+09:00","_attributeFile":{"_content":"Sidney A. Morris"}}},"_answers":1},"_parentHash":"2aed5404c83f7a46aa249e0a6328af756b19d513","_childPageContents":[{"_pageTitle":"5. Continuous Mappings","_hash":"6c11e3a31b4b8bd07bdef3f87887ab202a568679","_attributes":{},"_answers":1}]}
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{
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"_childPageContents": [
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{
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"_answers": 1,
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"_attributes": {},
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"_hash": "6c11e3a31b4b8bd07bdef3f87887ab202a568679",
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"_pageTitle": "5. Continuous Mappings"
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}
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],
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"_pageContent": {
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"_answers": 1,
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"_attributes": {
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"author.txt": {
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"_attributeFile": {
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"_content": "Sidney A. Morris"
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},
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"_time": "2022-09-25T22:34:28+09:00"
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}
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},
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"_hash": "4c1513c92422dc16b3c5f13bd03d34ba0feeb6df",
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"_pageTitle": "Topology Without Tears"
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},
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"_parentHash": "2aed5404c83f7a46aa249e0a6328af756b19d513"
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}
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{"_pageContent":{"_pageTitle":"10. Natural Transformations","_hash":"54c6ff9a213b80284619a5afb7859d9d30a444bc","_attributes":{},"_answers":1},"_parentHash":"b614f31d04b3bc2b3d23ee4337475251429e5a9f","_childPageContents":[{"_pageTitle":"5","_hash":"ebe52014d6aaf02a4ddeaa7de59a014eac6634b8","_attributes":{"a.md":{"_time":"2020-10-18T14:48:51+09:00","_attributeFile":{"_content":"Let's proove interchange law.\n\n\n$`\\left( \\beta '\\cdot \\alpha '\\right) \\circ \\left( \\beta \\cdot \\alpha \\right) =\\left( \\beta '\\circ \\beta \\right) \\cdot \\left( \\alpha '\\circ \\alpha \\right)`$\n\n\nLet's say each natural transformation is defined as\n\n\n$`\\alpha :F\\rightarrow F_{2}`$\n$`\\alpha ':F_{2}\\rightarrow F_{3}`$\n$`\\beta :G\\rightarrow G_{2}`$\n$`\\beta ':G_{2}\\rightarrow G_{3}`$\n\n\n![](nat.JPG)\n\nLet's see what we get with first one.\n\n$`\\left( \\beta '\\cdot \\alpha '\\right) \\circ \\left( \\beta \\cdot \\alpha \\right)GF`$ \n\nUsing horizontal composition\n$`=\\left( \\beta'\\cdot \\alpha '\\right) G_{2}F_{2}`$\nAgain, using horizontal composition\n$`=G_{3}F_{3}`$\n\nNow the second one.\n\n$`\\left( \\beta '\\circ \\beta \\right) \\cdot \\left( \\alpha '\\circ \\alpha \\right)GF`$\n\nUnlike previous one, we cannot directly apply the $`(\\alpha' \\circ \\alpha)`$ to $`GF`$. No problem. We can composite horizontally with $`id:G\\rightarrow G`$\n\n$`=\\left( \\beta '\\circ \\beta\\right) \\cdot \\left( \\left( id\\cdot \\alpha '\\right) \\circ \\left( id\\cdot \\alpha \\right) \\right)GF`$\n$`=\\left( \\beta'\\circ \\beta\\right)GF_3`$\n\nSame way but this time with $`id:F\\rightarrow F`$\n\n$`=\\left( \\left( \\beta'\\cdot id\\right) \\circ \\left( \\beta \\cdot id\\right) \\right) GF_{3}`$\n$`=G_3 F_3`$\n\n\nProooven BAMMM"}},"q.md":{"_time":"2019-12-19T21:51:08+09:00","_attributeFile":{"_content":"Write a short essay about how you may enjoy writing down the evident diagrams needed to prove the interchange law.\n"}}},"_answers":1}]}
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{
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"_childPageContents": [
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{
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"_answers": 1,
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"_attributes": {
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"a.md": {
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"_attributeFile": {
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"_content": "Let's proove interchange law.\n\n\n$`\\left( \\beta '\\cdot \\alpha '\\right) \\circ \\left( \\beta \\cdot \\alpha \\right) =\\left( \\beta '\\circ \\beta \\right) \\cdot \\left( \\alpha '\\circ \\alpha \\right)`$\n\n\nLet's say each natural transformation is defined as\n\n\n$`\\alpha :F\\rightarrow F_{2}`$\n$`\\alpha ':F_{2}\\rightarrow F_{3}`$\n$`\\beta :G\\rightarrow G_{2}`$\n$`\\beta ':G_{2}\\rightarrow G_{3}`$\n\n\n![](nat.JPG)\n\nLet's see what we get with first one.\n\n$`\\left( \\beta '\\cdot \\alpha '\\right) \\circ \\left( \\beta \\cdot \\alpha \\right)GF`$ \n\nUsing horizontal composition\n$`=\\left( \\beta'\\cdot \\alpha '\\right) G_{2}F_{2}`$\nAgain, using horizontal composition\n$`=G_{3}F_{3}`$\n\nNow the second one.\n\n$`\\left( \\beta '\\circ \\beta \\right) \\cdot \\left( \\alpha '\\circ \\alpha \\right)GF`$\n\nUnlike previous one, we cannot directly apply the $`(\\alpha' \\circ \\alpha)`$ to $`GF`$. No problem. We can composite horizontally with $`id:G\\rightarrow G`$\n\n$`=\\left( \\beta '\\circ \\beta\\right) \\cdot \\left( \\left( id\\cdot \\alpha '\\right) \\circ \\left( id\\cdot \\alpha \\right) \\right)GF`$\n$`=\\left( \\beta'\\circ \\beta\\right)GF_3`$\n\nSame way but this time with $`id:F\\rightarrow F`$\n\n$`=\\left( \\left( \\beta'\\cdot id\\right) \\circ \\left( \\beta \\cdot id\\right) \\right) GF_{3}`$\n$`=G_3 F_3`$\n\n\nProooven BAMMM"
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},
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"_time": "2020-10-18T14:48:51+09:00"
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},
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"q.md": {
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"_attributeFile": {
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"_content": "Write a short essay about how you may enjoy writing down the evident diagrams needed to prove the interchange law.\n"
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},
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"_time": "2019-12-19T21:51:08+09:00"
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"_pageTitle": "10. Natural Transformations"
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