List questions from compactness

Published on 01 Oct 2016 - 18:54

552

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Is any necessary and sufficient criteria for a topological space to be compact using continuous functions?

Published on 02 Oct 2016 - 4:20

2k

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An infinite dimensional normed vector space is closed and bounded, but not compact

Published on 28 Mar 2026 - 14:55

766

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compact set of real numbers whose limit points form a countable set

Published on 03 Oct 2016 - 23:13

37

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Solutions starting at nearby points remain close to each other

Published on 04 Oct 2016 - 19:50

40

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Example of set in $\mathbb{R}^{2}$ that is compact but not $C$-compact

Published on 05 Oct 2016 - 23:40

82

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Why is this set open? How to prove it?

Published on 06 Oct 2016 - 9:43

52

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If $f: X \rightarrow Y$ is a bijection, then $f(U) = Y\setminus f(X \setminus U)$.

Published on 06 Oct 2016 - 23:27

141

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Group acts on a topological space

Published on 30 Mar 2026 - 8:19

98

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Are the following sets compact:

Published on 08 Oct 2016 - 15:28

335

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A sequence in a family of continuous functions over a $\sigma$-compact metric space has a uniformly convergent subsequence

Published on 23 Feb 2026 - 8:59

1k

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Is an expanding map on a compact metric space continuous?

Published on 09 Oct 2016 - 14:35

33

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Question About Compactness

Published on 09 Oct 2016 - 20:19

225

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Compact set whose closure isn't compact?

Published on 10 Oct 2016 - 15:57

50

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How to show that $int(cl(B_{n}))$ is non-empty if $X$ is compact space

Published on 29 Mar 2026 - 8:57

List Question

4 little questions on compactness and Hausdorffness

Is any necessary and sufficient criteria for a topological space to be compact using continuous functions?

An infinite dimensional normed vector space is closed and bounded, but not compact

compact set of real numbers whose limit points form a countable set

Solutions starting at nearby points remain close to each other

Example of set in $\mathbb{R}^{2}$ that is compact but not $C$-compact

Why is this set open? How to prove it?

If $f: X \rightarrow Y$ is a bijection, then $f(U) = Y\setminus f(X \setminus U)$.

Group acts on a topological space

Are the following sets compact:

A sequence in a family of continuous functions over a $\sigma$-compact metric space has a uniformly convergent subsequence

Is an expanding map on a compact metric space continuous?

Question About Compactness

Compact set whose closure isn't compact?

How to show that $int(cl(B_{n}))$ is non-empty if $X$ is compact space

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