Question

Problem with Rudin's proof that $\operatorname{diam}\mkern2mu\overline{\mkern-2muE}=\operatorname{diam}\text{ }E$

score 86 · Answer 1 · 2026-03-30 01:52:06

86

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Problem with Rudin's proof that $\operatorname{diam}\mkern2mu\overline{\mkern-2muE}=\operatorname{diam}\text{ }E$

Published on 30 Mar 2026 - 1:52

score 77 · Answer 2 · 2026-03-24 20:43:00

77

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If $Y=\left\{(x_i)\in\prod_i X_i| \{i\in I:x_i≠ p_i\} \text{ is finite}\right\}$ and $Y_F=\{(x_i)\in\prod_i X_i| i∉ F:x_i=p_i\}$ then $\bigcup Y_F=Y$

Published on 24 Mar 2026 - 20:43

score 1.1k · Answer 3 · 2026-03-30 01:52:02

1.1k

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Show that $Y$ is compact iff every collection of open sets in $X$ that covers $Y$ has a finite subcover.

Published on 30 Mar 2026 - 1:52

score 103 · Answer 4 · 2026-03-24 04:02:54

103

Views

Show that $(X,d)$ is compact

Published on 24 Mar 2026 - 4:02

score 63 · Answer 5 · 2026-03-20 08:56:10

63

Views

Is there a version of closing lemma in the case of uniform space?

Published on 20 Mar 2026 - 8:56

score 2.5k · Answer 6 · 2026-03-27 18:27:42

2.5k

Views

Let $(X, d)$ be a metric space. Prove that for every $r > 0$ and $x\in X$ that $\overline{\rm S_r(x)} \subseteq B_r(x)$

Published on 27 Mar 2026 - 18:27

score 42 · Answer 7 · 2026-03-26 07:34:45

42

Views

Parallels between subspaces of vector spaces, and closed sets: result of formal logic?

Published on 26 Mar 2026 - 7:34

score 928 · Answer 8 · 2018-02-28 06:36:28

928

Views

Separate two connected components of a closed set in a plane

Published on 28 Feb 2018 - 6:36

score 287 · Answer 9 · 2018-02-28 06:55:38

287

Views

Why do we care about quotient maps?

Published on 28 Feb 2018 - 6:55

score 204 · Answer 10 · 2026-03-30 01:46:42

204

Views

every bijection is an homeomorphism

Published on 30 Mar 2026 - 1:46

score 181 · Answer 11 · 2018-02-28 10:35:46

181

Views

Closure of A consist of every point of A including the set of all limits of convergent subsequences of A.

Published on 28 Feb 2018 - 10:35

score 112 · Answer 12 · 2026-03-27 18:34:35

112

Views

Topological Basis: Equivlance of Definitions

Published on 27 Mar 2026 - 18:34

score 488 · Answer 13 · 2018-02-28 11:21:24

488

Views

How to show that X is connected ?

Published on 28 Feb 2018 - 11:21

score 208 · Answer 14 · 2018-02-28 12:10:46

208

Views

Understanding why this lemma is useful (Lindelöf's Lemma).

Published on 28 Feb 2018 - 12:10

score 42 · Answer 15 · 2026-03-30 01:51:42

42

Views

Comparing Topologies of Metric Spaces

Published on 30 Mar 2026 - 1:51

List Question

Problem with Rudin's proof that $\operatorname{diam}\mkern2mu\overline{\mkern-2muE}=\operatorname{diam}\text{ }E$

If $Y=\left\{(x_i)\in\prod_i X_i| \{i\in I:x_i≠ p_i\} \text{ is finite}\right\}$ and $Y_F=\{(x_i)\in\prod_i X_i| i∉ F:x_i=p_i\}$ then $\bigcup Y_F=Y$

Show that $Y$ is compact iff every collection of open sets in $X$ that covers $Y$ has a finite subcover.

Show that $(X,d)$ is compact

Is there a version of closing lemma in the case of uniform space?

Let $(X, d)$ be a metric space. Prove that for every $r > 0$ and $x\in X$ that $\overline{\rm S_r(x)} \subseteq B_r(x)$

Parallels between subspaces of vector spaces, and closed sets: result of formal logic?

Separate two connected components of a closed set in a plane

Why do we care about quotient maps?

every bijection is an homeomorphism

Closure of A consist of every point of A including the set of all limits of convergent subsequences of A.

Topological Basis: Equivlance of Definitions

How to show that X is connected ?

Understanding why this lemma is useful (Lindelöf's Lemma).

Comparing Topologies of Metric Spaces

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