Question

A question on the purpose of the condition on hausdorff to prove homeomorphism

score 154 · Answer 1 · 2014-08-11 23:58:54

154

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A question on the purpose of the condition on hausdorff to prove homeomorphism

Published on 11 Aug 2014 - 23:58

score 1.6k · Answer 2 · 2014-08-12 14:07:38

1.6k

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Proof of compactness for sets of norm equal to one in finite-dimensional normed vector spaces

Published on 12 Aug 2014 - 14:07

score 507 · Answer 3 · 2026-03-29 06:55:52

507

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Clarifications on proof of compactness theorem

Published on 29 Mar 2026 - 6:55

score 620 · Answer 4 · 2026-03-30 23:13:33

620

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Does the converse of Tychonoff's theorem hinge on the axiom of choice?

Published on 30 Mar 2026 - 23:13

score 1.1k · Answer 5 · 2026-03-31 20:27:05

1.1k

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In a non-Hausdorff space, can a compact subset fail to be closed?

Published on 31 Mar 2026 - 20:27

score 3.7k · Answer 6 · 2014-08-14 11:14:41

3.7k

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Show that a finite union of compact subspaces of a topological space $X$ is compact.

Published on 14 Aug 2014 - 11:14

score 117 · Answer 7 · 2014-08-14 20:42:00

117

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If a property holds for arbitrary compact set in a metric space, does it also holds for the metric space?

Published on 14 Aug 2014 - 20:42

score 104 · Answer 8 · 2014-08-17 21:20:04

104

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Boundedness of continuous functions on compact sets

Published on 17 Aug 2014 - 21:20

score 252 · Answer 9 · 2026-03-25 14:31:40

252

Views

Showing that a space is normal and not locally compact

Published on 25 Mar 2026 - 14:31

score 756 · Answer 10 · 2026-03-25 14:33:43

756

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A continuous bijection from a Hausdorff space to a non-compact space which is not a homeomorphism

Published on 25 Mar 2026 - 14:33

score 412 · Answer 11 · 2026-03-25 14:38:01

412

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Infinite spaces in which all subsets are compact are not Hausdorff

Published on 25 Mar 2026 - 14:38

score 3.5k · Answer 12 · 2014-08-21 02:48:50

3.5k

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Non-compactness of $\mathbb{R}$ with the cocountable topology

Published on 21 Aug 2014 - 2:48

score 77 · Answer 13 · 2026-03-25 14:34:30

77

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A countable, compact KC-subspace of a hereditarily Lindelöf minimal KC-space

Published on 25 Mar 2026 - 14:34

score 1.8k · Answer 14 · 2026-03-25 23:36:23

1.8k

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Local compactness is preserved under continuous open onto mappings

Published on 25 Mar 2026 - 23:36

score 435 · Answer 15 · 2014-08-24 17:25:15

435

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Two definitions of compact set

Published on 24 Aug 2014 - 17:25

List Question

A question on the purpose of the condition on hausdorff to prove homeomorphism

Proof of compactness for sets of norm equal to one in finite-dimensional normed vector spaces

Clarifications on proof of compactness theorem

Does the converse of Tychonoff's theorem hinge on the axiom of choice?

In a non-Hausdorff space, can a compact subset fail to be closed?

Show that a finite union of compact subspaces of a topological space $X$ is compact.

If a property holds for arbitrary compact set in a metric space, does it also holds for the metric space?

Boundedness of continuous functions on compact sets

Showing that a space is normal and not locally compact

A continuous bijection from a Hausdorff space to a non-compact space which is not a homeomorphism

Infinite spaces in which all subsets are compact are not Hausdorff

Non-compactness of $\mathbb{R}$ with the cocountable topology

A countable, compact KC-subspace of a hereditarily Lindelöf minimal KC-space

Local compactness is preserved under continuous open onto mappings

Two definitions of compact set

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