List questions from compactness

Published on 11 Apr 2026 - 6:44

590

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Continuous bijection is a homeomorphism

Published on 17 Oct 2015 - 1:27

244

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Compactness of a family of closed subsets in a compact space.

Published on 26 Feb 2026 - 23:57

77

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$\beta\mathbb{N}$ is embedded in $\beta\mathbb{R}$

Published on 23 Mar 2026 - 3:52

95

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If $K \subset \mathbb{R}^2$ is compact, then $K$ is closed?

Published on 01 Apr 2026 - 0:57

533

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Can you recommend me a book about compactness (Real Analysis)?

Published on 06 Apr 2026 - 3:14

71

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If $\displaystyle\bigcap_{n\in\mathbb{N}} U_n=\{x\}$, then $\{U_1,U_2,...\}$ is a local base at $x$.

Published on 16 Apr 2026 - 11:46

143

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If each $X_n$ is countably compact then so is $\displaystyle\prod_{n\in\mathbb{N}}X_n$.

Published on 16 Apr 2026 - 22:17

51

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If $A$ is clopen in $X$ then $\overline{A}$ is clopen in $\beta X$.

Published on 16 Apr 2026 - 22:16

100

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Definition of One-point compactification

Published on 02 Apr 2026 - 23:05

408

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How to show a set is a norm compact subset

Published on 11 Apr 2026 - 8:19

143

Views

Compactness of $\mathbb{R}^n$

Published on 20 Oct 2015 - 8:38

233

Views

Is every countably compact Hausdorff space compact?

Published on 09 Apr 2026 - 9:56

116

Views

A "Simple Chain of Regions" and Compactness in the Continuum

Published on 13 Apr 2026 - 14:28

418

Views

prove that intersection of the family of the set is connected

Published on 22 Oct 2015 - 3:03

List Question

Proving non compactness of a space

Continuous bijection is a homeomorphism

Compactness of a family of closed subsets in a compact space.

$\beta\mathbb{N}$ is embedded in $\beta\mathbb{R}$

If $K \subset \mathbb{R}^2$ is compact, then $K$ is closed?

Can you recommend me a book about compactness (Real Analysis)?

If $\displaystyle\bigcap_{n\in\mathbb{N}} U_n=\{x\}$, then $\{U_1,U_2,...\}$ is a local base at $x$.

If each $X_n$ is countably compact then so is $\displaystyle\prod_{n\in\mathbb{N}}X_n$.

If $A$ is clopen in $X$ then $\overline{A}$ is clopen in $\beta X$.

Definition of One-point compactification

How to show a set is a norm compact subset

Compactness of $\mathbb{R}^n$

Is every countably compact Hausdorff space compact?

A "Simple Chain of Regions" and Compactness in the Continuum

prove that intersection of the family of the set is connected

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