List questions from compactness

Published on 15 Apr 2026 - 14:32

119

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Space filling curves: Hilbert vs Peano

Published on 14 Apr 2026 - 2:07

89

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compactness and relative compactness

Published on 12 Apr 2026 - 23:54

184

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Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets

Published on 10 May 2026 - 16:12

710

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Show that given a proper map, for each closed set F its image f(F) is closed

Published on 11 May 2026 - 4:20

98

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Characterize the compact subspaces in a topological space.

Published on 15 Apr 2026 - 1:28

1.6k

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Proving $\mathbb{N}$ is not compact

Published on 11 Apr 2026 - 20:29

109

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Is $\mathbb{Q} \cap (a,b)$ for irrationals $a,b$ is not compact in the $\mathbb{Q}$ with $d(x,y)=|x-y|$?

Published on 16 Apr 2026 - 5:43

1.6k

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Is $[ \sqrt 2, \sqrt 3] \cap \mathbb{Q}$ an open subset of $\mathbb{Q}$?

Published on 14 Apr 2026 - 18:10

19k

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Continuous bijection between compact and Hausdorff spaces is a homeomorphism

Published on 09 Apr 2026 - 9:09

352

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Show that if two metrics induce the same topology, one metric space is compact iff the other one is.

Published on 15 Apr 2026 - 4:13

129

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Contradiction in the proof a space with every compact subspace is not Hausdorff

Published on 10 May 2026 - 19:35

77

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Topology in $\Bbb {R}^n$ Proof Exercise

Published on 12 Apr 2026 - 19:16

327

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Must compact bijections be continuous?

Published on 09 Apr 2026 - 21:23

81

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How to show a continuous function in the reals maps compact sets into compact sets?

Published on 11 Apr 2026 - 0:05

List Question

$A$ is compact and closed then prove ...

Space filling curves: Hilbert vs Peano

compactness and relative compactness

Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets

Show that given a proper map, for each closed set F its image f(F) is closed

Characterize the compact subspaces in a topological space.

Proving $\mathbb{N}$ is not compact

Is $\mathbb{Q} \cap (a,b)$ for irrationals $a,b$ is not compact in the $\mathbb{Q}$ with $d(x,y)=|x-y|$?

Is $[ \sqrt 2, \sqrt 3] \cap \mathbb{Q}$ an open subset of $\mathbb{Q}$?

Continuous bijection between compact and Hausdorff spaces is a homeomorphism

Show that if two metrics induce the same topology, one metric space is compact iff the other one is.

Contradiction in the proof a space with every compact subspace is not Hausdorff

Topology in $\Bbb {R}^n$ Proof Exercise

Must compact bijections be continuous?

How to show a continuous function in the reals maps compact sets into compact sets?

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