Example 1 Let \(X\) be the subspace \([0,1]\cup[2,3]\) of \(\mathbb{R}\), and let \(Y\) be the subspace \([0,2]\) of \(\mathbb{R}\). The map \(p: X \r... ...
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其他好文 时间：
2019-02-09 19:18:31
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Exercise 22.3 Let \(\pi_1: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}\) be projection on the first coordinate. Let \(A\) be the subspace of \ ...
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2019-02-09 19:13:55
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Lemma 21.2 (The sequence lemma) Let \(X\) be a topological space; let \(A \subset X\). If there is a sequence of points of \(A\) converging to \(x\), ... ...
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2019-01-20 14:00:14
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Theorem 20.4 The uniform topology on \(\mathbb{R}^J\) is finer than the product topology and coarser than the box topology; these three topologies are... ...
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2019-01-05 00:14:12
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绘制拓扑图有很多开源的工具,知乎上也有人回答了这个问题: https://www.zhihu.com/question/41026400/answer/118726253 ujtopo是基于jTopo作了一些封装,适用一些基本的场景 jTopo（Javascript Topology library ...
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2018-12-29 11:13:08
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253
Theorem 19.6 Let \(f: A \rightarrow \prod_{\alpha \in J} X_{\alpha}\) be given by the equation\[f(a) = (f_{\alpha}(a))_{\alpha \in J},\]where \(f_{\al... ...
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2018-12-23 19:30:36
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This post summarises different ways of constructing continuous functions, which are introduced in Section 18 of James Munkres “Topology”.Constant func... ...
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2018-12-19 18:40:24
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115
Theorem 18.4 in James Munkres “Topology” states that if a function \(f : A \rightarrow X \times Y\) is continuous, its coordinate functions \(f_1 : A ...
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2018-12-18 22:38:34
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Understanding of continuity definition in topology When we learn calculus in university as freshmen, we are usually force-fed with the \(\epsilon-\del ...
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2018-12-15 23:52:52
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Theorem 16.3 If \(A\) is a subspace of \(X\) and \(B\) is a subspace of \(Y\), then the product topology on \(A \times B\) is the same as the topology ...
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2018-12-14 01:07:42
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