List questions from compactness

Published on 27 Oct 2016 - 21:37

232

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Disjoint sets $A,B$ with $d(A,B) = 0$ in a metric space $M$ compact imply that $\partial A \cap \partial B \neq \emptyset$

Published on 28 Oct 2016 - 3:16

71

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Compactness of the set in $\mathbb{R}$

Published on 28 Oct 2016 - 11:38

63

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Pedagogical use cases of compactness

Published on 28 Oct 2016 - 15:05

228

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Quotients of extremally disconnected compact Hausdorff spaces

Published on 02 Apr 2026 - 9:34

1.9k

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Does compactness depend on the metric?

Published on 31 Oct 2016 - 2:13

746

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Compact subset of the space of all bounded sequences of real numbers

Published on 29 Mar 2026 - 15:54

64

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Sufficient condition for a Topological space to be Hausdorff

Published on 01 Nov 2016 - 21:38

113

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Locally finite compact metric space

Published on 02 Nov 2016 - 9:47

65

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Compactness/ Non-Compactness of $\left\{\tan(1/n): n\in\mathbb{N}\right\}\cap [0,1]\subset\mathbb{R}$

Published on 02 Nov 2016 - 14:46

47

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About a special case of continuity in cartesian product of compacts result

Published on 03 Nov 2016 - 14:57

241

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Is every metric space realcompact?

Published on 01 Apr 2026 - 12:42

310

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Where do we need compactness in this proof?

Published on 03 Nov 2016 - 20:09

194

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Prove that a subset G of $C([0,\pi])$ is relatively compact in $C([0,\pi])$

Published on 23 Feb 2026 - 8:59

158

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Prove the two definitions of relative sequential compactness are equivalent if X is first-countable.

Published on 06 Nov 2016 - 16:09

List Question

The elements of a closed set and compact set form a closed set.

Disjoint sets $A,B$ with $d(A,B) = 0$ in a metric space $M$ compact imply that $\partial A \cap \partial B \neq \emptyset$

Compactness of the set in $\mathbb{R}$

Pedagogical use cases of compactness

Quotients of extremally disconnected compact Hausdorff spaces

Does compactness depend on the metric?

Compact subset of the space of all bounded sequences of real numbers

Sufficient condition for a Topological space to be Hausdorff

Locally finite compact metric space

Compactness/ Non-Compactness of $\left\{\tan(1/n): n\in\mathbb{N}\right\}\cap [0,1]\subset\mathbb{R}$

About a special case of continuity in cartesian product of compacts result

Is every metric space realcompact?

Where do we need compactness in this proof?

Prove that a subset G of $C([0,\pi])$ is relatively compact in $C([0,\pi])$

Prove the two definitions of relative sequential compactness are equivalent if X is first-countable.

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