Question

$x_n \rightarrow x \implies \lim_{n \rightarrow +\infty}$ IFF $f_n \rightarrow f$ uniformly in each $K \subset M$ compact

score 496 · Answer 1 · 2026-04-18 05:23:58

496

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$x_n \rightarrow x \implies \lim_{n \rightarrow +\infty}$ IFF $f_n \rightarrow f$ uniformly in each $K \subset M$ compact

Published on 18 Apr 2026 - 5:23

score 299 · Answer 2 · 2026-04-13 14:47:18

299

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Equivalence of uniform convergence in metric spaces!

Published on 13 Apr 2026 - 14:47

score 3.2k · Answer 3 · 2026-04-01 17:32:49

3.2k

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For uniformly continuous $f:X\to Y$, where $X$ is a totally bounded metric space, prove that $f(X)$ is totally bounded

Published on 01 Apr 2026 - 17:32

score 217 · Answer 4 · 2026-04-11 21:42:52

217

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Finding an open cover without finite sub cover

Published on 11 Apr 2026 - 21:42

score 1.4k · Answer 5 · 2026-03-30 02:10:31

1.4k

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Show a continuous function on a closed bounded interval is Lipschitz under the maximum (infinity) norm

Published on 30 Mar 2026 - 2:10

score 1k · Answer 6 · 2026-04-09 04:08:35

1k

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How to prove that $A \cap B$ is compact using the definition of compact set

Published on 09 Apr 2026 - 4:08

score 53 · Answer 7 · 2026-04-11 00:43:15

53

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Compactness on set with two topologies

Published on 11 Apr 2026 - 0:43

score 56 · Answer 8 · 2026-04-10 17:41:09

56

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Proving a set is compact!

Published on 10 Apr 2026 - 17:41

score 538 · Answer 9 · 2015-12-09 23:58:20

538

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Let $X$ locally compact, Hausdorff and non compact. Ends.

Published on 09 Dec 2015 - 23:58

score 796 · Answer 10 · 2026-04-15 03:58:44

796

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One point compactification, Hausdorff space in which every point has a compact neighborhood. Show $X'=X\cup\{\infty\}$ is compact and connected

Published on 15 Apr 2026 - 3:58

score 217 · Answer 11 · 2015-12-11 00:24:50

217

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Compact space - definition

Published on 11 Dec 2015 - 0:24

score 94 · Answer 12 · 2026-04-14 18:08:59

94

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T/F: The set: $\{(x,y): \sin(x^{2012} +y^3) + x^2 + y^4 \le 1\}$ is a compact set in $\mathbb{R}^2$.

Published on 14 Apr 2026 - 18:08

score 892 · Answer 13 · 2026-04-12 19:17:00

892

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Topology: Difference between Bolzano-Weierstrass Property and Sequential Compactness?

Published on 12 Apr 2026 - 19:17

score 164 · Answer 14 · 2015-12-12 21:04:24

164

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Compact connected space is the union of two disjoint connected sets.

Published on 12 Dec 2015 - 21:04

score 343 · Answer 15 · 2026-04-13 18:28:44

343

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Kuratowski measure of non-compactness of unit ball and unit sphere.

Published on 13 Apr 2026 - 18:28

List Question

$x_n \rightarrow x \implies \lim_{n \rightarrow +\infty}$ IFF $f_n \rightarrow f$ uniformly in each $K \subset M$ compact

Equivalence of uniform convergence in metric spaces!

For uniformly continuous $f:X\to Y$, where $X$ is a totally bounded metric space, prove that $f(X)$ is totally bounded

Finding an open cover without finite sub cover

Show a continuous function on a closed bounded interval is Lipschitz under the maximum (infinity) norm

How to prove that $A \cap B$ is compact using the definition of compact set

Compactness on set with two topologies

Proving a set is compact!

Let $X$ locally compact, Hausdorff and non compact. Ends.

One point compactification, Hausdorff space in which every point has a compact neighborhood. Show $X'=X\cup\{\infty\}$ is compact and connected

Compact space - definition

T/F: The set: $\{(x,y): \sin(x^{2012} +y^3) + x^2 + y^4 \le 1\}$ is a compact set in $\mathbb{R}^2$.

Topology: Difference between Bolzano-Weierstrass Property and Sequential Compactness?

Compact connected space is the union of two disjoint connected sets.

Kuratowski measure of non-compactness of unit ball and unit sphere.

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