List questions from compactness

Published on 15 Apr 2026 - 10:58

211

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Regularly open, co-zero sets in compact Hausdorff spaces

Published on 11 Apr 2026 - 10:46

113

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Exercise I.7.2 in Geometry and Topology by Bredon

Published on 16 Apr 2026 - 15:45

46

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compactness of thes sequence set

Published on 13 Apr 2026 - 16:11

70

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How does the compactness property help us show a subset $A$ of a metric space $X$ is closed?

Published on 12 Apr 2026 - 17:16

715

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Non-compact subsets of a metric space $(X,d)$.

Published on 15 Apr 2026 - 3:51

404

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Question on proof of unit ball in $C([0, 1])$ not being compact

Published on 12 Apr 2026 - 10:43

949

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$K$ compact metric space, is there a finite set of continuous functions that separates points in $K$?

Published on 15 Apr 2026 - 10:25

1.2k

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Prove that any continuous bijection $f:X \rightarrow Y$ from a compact space $X$ to a Hausdorff space $Y$ is a homeomorphism

Published on 13 Apr 2026 - 18:14

84

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Compact subsets of a Hausdorff space

Published on 12 Apr 2026 - 2:13

396

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Homeomorphic but not equivalent compactifications.

Published on 12 Apr 2026 - 6:19

307

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Urysohn's Lemma, Stone-Weierstrass

Published on 14 Apr 2026 - 12:13

370

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What is a finite subcover of $[0,1]^{[0,1]}$?

Published on 10 Apr 2026 - 19:43

3.8k

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Open interval $(0,1)$ is totally bounded

Published on 11 Apr 2026 - 18:35

136

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Is Inverse of a function continuous too?

Published on 11 Apr 2026 - 10:48

List Question

Showing a metric space is not complete.

Regularly open, co-zero sets in compact Hausdorff spaces

Exercise I.7.2 in Geometry and Topology by Bredon

compactness of thes sequence set

How does the compactness property help us show a subset $A$ of a metric space $X$ is closed?

Non-compact subsets of a metric space $(X,d)$.

Question on proof of unit ball in $C([0, 1])$ not being compact

$K$ compact metric space, is there a finite set of continuous functions that separates points in $K$?

Prove that any continuous bijection $f:X \rightarrow Y$ from a compact space $X$ to a Hausdorff space $Y$ is a homeomorphism

Compact subsets of a Hausdorff space

Homeomorphic but not equivalent compactifications.

Urysohn's Lemma, Stone-Weierstrass

What is a finite subcover of $[0,1]^{[0,1]}$?

Open interval $(0,1)$ is totally bounded

Is Inverse of a function continuous too?

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