Question

The space of sequence is infinite dimensional yet it seems Bolzano-Weiestrass applies

score 44 · Answer 1 · 2026-04-12 17:37:22

44

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The space of sequence is infinite dimensional yet it seems Bolzano-Weiestrass applies

Published on 12 Apr 2026 - 17:37

score 67 · Answer 2 · 2026-04-13 19:40:00

67

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How do I show that $\text{dist}(x,A)=\varepsilon + \text{dist}(x,B_{\varepsilon}(A))$, if $\text{dist}(x,A)\gt \varepsilon$?

Published on 13 Apr 2026 - 19:40

score 54 · Answer 3 · 2026-04-14 12:01:48

Is A = $\{(0,0)\}\cup \{(x,\sin(1/x))|0 < x \le 1\}$ $\subseteq \mathbb{R}^2$ under the usual metric on $\mathbb{R}$ is compact?

score 116 · Answer 4 · 2026-04-14 03:19:54

116

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Why is a categorical product in Top uniquely equal to the product topology?

Published on 14 Apr 2026 - 3:19

score 835 · Answer 5 · 2026-04-29 12:56:29

835

Views

Equivalence of Baire Category Theorem for Complete Metric Spaces.

Published on 29 Apr 2026 - 12:56

score 59 · Answer 6 · 2026-04-29 12:25:55

59

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Left homotopy groups

Published on 29 Apr 2026 - 12:25

score 77 · Answer 7 · 2026-04-14 21:17:09

77

Views

A non-polyhedral pair $(X,A)$ with both $X$ and $A$ polyhedral

Published on 14 Apr 2026 - 21:17

score 284 · Answer 8 · 2026-04-14 09:40:49

284

Views

Formula for relative homotopy groups of products

Published on 14 Apr 2026 - 9:40

score 33 · Answer 9 · 2026-04-14 06:42:55

33

Views

Is there a nonHausdorff topology on $\mathbb{R}$ such that we still have the closedness/boundedness equivalence to compactness?

Published on 14 Apr 2026 - 6:42

score 95 · Answer 10 · 2026-04-10 00:38:05

95

Views

Is there a metric with wildcard?

Published on 10 Apr 2026 - 0:38

score 121 · Answer 11 · 2026-04-16 07:15:09

121

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Smash product of $I_+$ with a space $X$

Published on 16 Apr 2026 - 7:15

score 61 · Answer 12 · 2026-04-14 19:04:22

61

Views

Intersection of a closed and a dense subset of a Compact Hausdorff space be empty?

Published on 14 Apr 2026 - 19:04

score 116 · Answer 13 · 2026-04-11 02:20:45

116

Views

Course recommendation if I Iiked Analysis and Topology

Published on 11 Apr 2026 - 2:20

score 152 · Answer 14 · 2026-04-11 21:35:55

152

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Approximating a continuous function by a sawtooth function

Published on 11 Apr 2026 - 21:35

score 211 · Answer 15 · 2026-04-13 02:02:24

211

Views

Example of a connected topological space with an open singleton set

Published on 13 Apr 2026 - 2:02

List Question

The space of sequence is infinite dimensional yet it seems Bolzano-Weiestrass applies

How do I show that $\text{dist}(x,A)=\varepsilon + \text{dist}(x,B_{\varepsilon}(A))$, if $\text{dist}(x,A)\gt \varepsilon$?

Is A = $\{(0,0)\}\cup \{(x,\sin(1/x))|0 < x \le 1\}$ $\subseteq \mathbb{R}^2$ under the usual metric on $\mathbb{R}$ is compact?

Why is a categorical product in Top uniquely equal to the product topology?

Equivalence of Baire Category Theorem for Complete Metric Spaces.

Left homotopy groups

A non-polyhedral pair $(X,A)$ with both $X$ and $A$ polyhedral

Formula for relative homotopy groups of products

Is there a nonHausdorff topology on $\mathbb{R}$ such that we still have the closedness/boundedness equivalence to compactness?

Is there a metric with wildcard?

Smash product of $I_+$ with a space $X$

Intersection of a closed and a dense subset of a Compact Hausdorff space be empty?

Course recommendation if I Iiked Analysis and Topology

Approximating a continuous function by a sawtooth function

Example of a connected topological space with an open singleton set

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