List questions from compactness

Published on 25 Feb 2026 - 2:28

75

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Prove space of strict contractions is closed

Published on 23 Feb 2026 - 10:47

102

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Proof of Heine-Borel theorem; Hunter

Published on 21 Jun 2023 - 20:59

42

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The nonnegative set of compact subset of $L^p$ is compact.

Published on 24 Jun 2023 - 14:53

37

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Subcovering of a finite ball-covering of compact sets.

Published on 25 Jun 2023 - 21:06

48

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A sub-covering consisted of compact sets which are subsets of the original open covering

Published on 26 Jun 2023 - 0:01

59

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Alternative proof: Metric space is compact iff it's sequentially compact.

Published on 26 Jun 2023 - 12:19

60

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If $X$ is compact Hausdorf and $A$ is closed than $Y=A^c$ is locally compact

Published on 26 Jun 2023 - 17:29

123

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Is every Lindelöf space Menger?

Published on 27 Mar 2026 - 12:56

116

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Space of smooth differential forms with compact support on $U \subset \mathbb{R}^n$ is separable

Published on 26 Mar 2026 - 14:42

96

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Compactness, pseudocompactness, and realcompactness without Hausdorff

Published on 23 Feb 2026 - 4:26

152

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Stone-Weierstrass theorem for non-polynomials

Published on 04 Jul 2023 - 23:18

84

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$L^1$ equicontinuity for functions with uniformly bounded total variation

Published on 27 Mar 2026 - 3:49

103

Views

Proof for this set to be compact

Published on 07 Jul 2023 - 11:33

110

Views

Universal property of one-point-compactification

Published on 26 Mar 2026 - 16:23

List Question

Examples of spaces where compact convergence is not equivalent to local uniform convergence.

Prove space of strict contractions is closed

Proof of Heine-Borel theorem; Hunter

The nonnegative set of compact subset of $L^p$ is compact.

Subcovering of a finite ball-covering of compact sets.

A sub-covering consisted of compact sets which are subsets of the original open covering

Alternative proof: Metric space is compact iff it's sequentially compact.

If $X$ is compact Hausdorf and $A$ is closed than $Y=A^c$ is locally compact

Is every Lindelöf space Menger?

Space of smooth differential forms with compact support on $U \subset \mathbb{R}^n$ is separable

Compactness, pseudocompactness, and realcompactness without Hausdorff

Stone-Weierstrass theorem for non-polynomials

$L^1$ equicontinuity for functions with uniformly bounded total variation

Proof for this set to be compact

Universal property of one-point-compactification

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