List questions from compactness

Published on 25 Mar 2026 - 15:26

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How to prove a property of sequentially compact sets

Published on 08 Jun 2018 - 3:26

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A first countable, countably compact space is sequentially compact

Published on 25 Mar 2026 - 1:37

112

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Munkres Analysis on Manifolds: Ex 1.3: Why does the example not contradict with the given theorem?

Published on 26 Mar 2026 - 8:04

678

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Compactness of set of Lipschitz functions $f:D\rightarrow D$

Published on 25 Mar 2026 - 6:35

123

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Is the projective space over matrices of rank bigger than $k$ compact?

Published on 25 Mar 2026 - 14:26

61

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How to show that the following set is compact.

Published on 25 Mar 2026 - 21:49

35

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A space $X$ with property that all compact subspaces are closed.

Published on 25 Mar 2026 - 0:02

42

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Is Any Finite Graph Structure G(V,E) Homeomorphic to Any Example of Compact Metrizable Space?

Published on 25 Mar 2026 - 16:01

52

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Is $(\Bbb N, \tau)$ a compact topological space?

Published on 13 Jun 2018 - 15:07

125

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Proof that $\overline{B}_1(0)$ is not compact in $(C[0,1],||\cdot||_{\infty})$

Published on 13 Jun 2018 - 18:22

435

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Compactness implies that every net has a converging subnet - why that definition of subnet?

Published on 17 Mar 2026 - 17:10

309

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Proof Verification: show that $[0,1] \cap \Bbb Q$ is not compact in the metric space $\Bbb Q$

Published on 15 Jun 2018 - 4:21

360

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Prove that lim$_{n \rightarrow \infty} (1 + \frac{z}{n})^{n} = e^z$ uniformly on all compact sets.

Published on 28 Mar 2026 - 8:36

151

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Sphere in $C^3$ is not compact?

Published on 15 Jun 2018 - 18:24

List Question

How to check the compactness of following sets?

How to prove a property of sequentially compact sets

A first countable, countably compact space is sequentially compact

Munkres Analysis on Manifolds: Ex 1.3: Why does the example not contradict with the given theorem?

Compactness of set of Lipschitz functions $f:D\rightarrow D$

Is the projective space over matrices of rank bigger than $k$ compact?

How to show that the following set is compact.

A space $X$ with property that all compact subspaces are closed.

Is Any Finite Graph Structure G(V,E) Homeomorphic to Any Example of Compact Metrizable Space?

Is $(\Bbb N, \tau)$ a compact topological space?

Proof that $\overline{B}_1(0)$ is not compact in $(C[0,1],||\cdot||_{\infty})$

Compactness implies that every net has a converging subnet - why that definition of subnet?

Proof Verification: show that $[0,1] \cap \Bbb Q$ is not compact in the metric space $\Bbb Q$

Prove that lim$_{n \rightarrow \infty} (1 + \frac{z}{n})^{n} = e^z$ uniformly on all compact sets.

Sphere in $C^3$ is not compact?

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