List questions from compactness

Published on 21 May 2014 - 21:57

268

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How to show $A=\{(x,y)\in R^2:4x^2+9y^2=36\}$ is path connected and compact?

Published on 30 Mar 2026 - 17:53

97

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An infinite compact set which allows no boundedness and analyticity

Published on 25 Mar 2026 - 9:47

1.3k

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How to "convert" from net to sequence in a first countable space

Published on 25 Mar 2026 - 9:23

145

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Is the set of translations of a function compact?

Published on 28 Mar 2026 - 8:09

174

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Approximation by finite sets

Published on 26 May 2014 - 17:13

86

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For compact subspaces $C$ and $K$ of $X$ and $Y$, prove that for every open set $U$ of $X \times Y$, there exist open sets $V$ and $W$ with...

Published on 28 May 2014 - 19:15

298

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Using the compactness theorem

Published on 30 May 2014 - 11:28

80

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A compactness result: if $f_n(u_n) \rightharpoonup w$ in $L^2(0,T;L^2)$, then $f_n(u_n) \to w$ in $L^2(s,T;H^{-1})$ for all $s > 0$.

Published on 25 Mar 2026 - 17:44

422

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Naive question about the group $SU(n)$?

Published on 30 May 2014 - 13:25

185

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Property of compact, convex sets in $\mathbb{R}^3$

Published on 30 May 2014 - 18:06

52

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Compact set in $(\mathbb R,\rho_1)$

Published on 01 Jun 2014 - 14:35

1.4k

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Cardinality of all compact metric spaces

Published on 28 Mar 2026 - 13:42

461

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Prove that a relatively compact subset of $L^p$ is bounded.

Published on 01 Apr 2026 - 0:24

4.4k

Views

Compactness and sequential compactness in metric spaces

Published on 05 Jun 2014 - 21:30

List Question

Topological distinguishibilty of $\infty$ after one point compactification?

How to show $A=\{(x,y)\in R^2:4x^2+9y^2=36\}$ is path connected and compact?

An infinite compact set which allows no boundedness and analyticity

How to "convert" from net to sequence in a first countable space

Is the set of translations of a function compact?

Approximation by finite sets

For compact subspaces $C$ and $K$ of $X$ and $Y$, prove that for every open set $U$ of $X \times Y$, there exist open sets $V$ and $W$ with...

Using the compactness theorem

A compactness result: if $f_n(u_n) \rightharpoonup w$ in $L^2(0,T;L^2)$, then $f_n(u_n) \to w$ in $L^2(s,T;H^{-1})$ for all $s > 0$.

Naive question about the group $SU(n)$?

Property of compact, convex sets in $\mathbb{R}^3$

Compact set in $(\mathbb R,\rho_1)$

Cardinality of all compact metric spaces

Prove that a relatively compact subset of $L^p$ is bounded.

Compactness and sequential compactness in metric spaces

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