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James Munkres Topology: Sec 22 Example 1
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... ...
分类:其他好文   时间:2019-02-09 19:18:31    阅读次数:124
James Munkres Topology: Sec 22 Exer 3
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 \ ...
分类:其他好文   时间:2019-02-09 19:13:55    阅读次数:154
James Munkres Topology: Lemma 21.2 The sequence lemma
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 \(x\), ... ...
分类:其他好文   时间:2019-01-20 14:00:14    阅读次数:124
James Munkres Topology: Theorem 20.4
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... ...
分类:其他好文   时间:2019-01-05 00:14:12    阅读次数:120
基于jTopo的拓扑图设计工具库ujtopo
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 ...
分类:其他好文   时间:2018-12-29 11:13:08    阅读次数:253
James Munkres Topology: Theorem 19.6
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... ...
分类:其他好文   时间:2018-12-23 19:30:36    阅读次数:133
Constructing continuous functions
This post summarises different ways of constructing continuous functions, which are introduced in Section 18 of James Munkres “Topology”.Constant func... ...
分类:其他好文   时间:2018-12-19 18:40:24    阅读次数:115
James Munkres Topology: Sec 18 Exer 12
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 ...
分类:其他好文   时间:2018-12-18 22:38:34    阅读次数:183
Concept of function continuity in topology
Understanding of continuity definition in topology When we learn calculus in university as freshmen, we are usually force-fed with the \(\epsilon-\del ...
分类:其他好文   时间:2018-12-15 23:52:52    阅读次数:177
James Munkres Topology: Theorem 16.3
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 ...
分类:其他好文   时间:2018-12-14 01:07:42    阅读次数:152
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