List questions from compactness

Published on 26 Mar 2026 - 8:03

158

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show that $K=[x_n, n \in N] \cup [l]$ is compact.Using only subsequences.

Published on 09 Nov 2019 - 6:06

78

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Show closedness , path connectedness and compactness

Published on 09 Nov 2019 - 19:49

362

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Is the union of a closed interval and half closed interval compact?

Published on 09 Nov 2019 - 22:04

215

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Is the subset 1/2^n compact?

Published on 10 Nov 2019 - 14:18

63

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Existence of ultrafilters in a compact subset.

Published on 11 Nov 2019 - 11:21

48

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existence of point $u,v\in A $ such that $d(u,v)=\sup\{d(x,y):x,y\in A\}$ holds.

Published on 29 Mar 2026 - 12:57

179

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About Lebesgue-measure and regularity.

Published on 25 Mar 2026 - 14:21

492

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Is the union of a countable number of disjoint compact sets never compact?

Published on 13 Nov 2019 - 20:34

515

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Doubt in proof of one point compactification of Locally Compact Hausdorff Space

Published on 14 Nov 2019 - 6:25

270

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Let $X$ be a locally compact ,Hausdorff space and $\{U_n\}$ be a sequence of dense open sets in $X$ .Show that $\cap_nU_n$ is dense in $X$.

Published on 16 Nov 2019 - 4:05

598

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Why is $X^$ with the weak- topology not a locally compact vector space?

Published on 26 Mar 2026 - 21:12

52

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Uniform Convergence on Compact Hausdorff Space

Published on 16 Nov 2019 - 13:07

182

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Topology: Proof by Induction.

Published on 16 Nov 2019 - 22:01

1.8k

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Proving that a compact Hausdorff space is a Baire space.

Published on 17 Nov 2019 - 4:57

List Question

Let $X$ be a countable set. Then which of the following are true?

show that $K=[x_n, n \in N] \cup [l]$ is compact.Using only subsequences.

Show closedness , path connectedness and compactness

Is the union of a closed interval and half closed interval compact?

Is the subset 1/2^n compact?

Existence of ultrafilters in a compact subset.

existence of point $u,v\in A $ such that $d(u,v)=\sup\{d(x,y):x,y\in A\}$ holds.

About Lebesgue-measure and regularity.

Is the union of a countable number of disjoint compact sets never compact?

Doubt in proof of one point compactification of Locally Compact Hausdorff Space

Let $X$ be a locally compact ,Hausdorff space and $\{U_n\}$ be a sequence of dense open sets in $X$ .Show that $\cap_nU_n$ is dense in $X$.

Why is $X^$ with the weak- topology not a locally compact vector space?

Uniform Convergence on Compact Hausdorff Space

Topology: Proof by Induction.

Proving that a compact Hausdorff space is a Baire space.

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