List questions from compactness

Published on 10 May 2026 - 15:24

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Third homotopy group of quotient space

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1) Is $\Bbb R \setminus \Bbb Q$ compact? 2) Prove $[0, 1] \times [0, 1]$ and $(0, 1) \times (0, 1)$ are not homeomorphic

Published on 15 Apr 2026 - 14:28

186

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How to prove the outer measure of a compact set in Rn is the infimum of sums of volumes of closed cubes?

Published on 11 May 2026 - 5:33

112

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Erwin kreyszig functional analysis Page.82 Ex.4

Published on 15 Apr 2026 - 23:06

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is compactness equivalent to limit point compactness?

Published on 09 Apr 2026 - 18:24

419

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Definition of relative (sequential) compactness

Published on 10 May 2026 - 14:04

90

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How to check continuous function $f$ has extension?

Published on 10 May 2026 - 21:17

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Compactness and connectedness of sets

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$f$ be real uniformly continuous function on the bounded set $E$ of $\Bbb R$ then $f$ is bounded on $E$

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Why we can assume compactness in Victor Klee's theorem?

Published on 14 Apr 2026 - 7:22

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Unit ball in $l^{2}$ is bounded and closed but not compact.

Published on 10 May 2026 - 17:37

100

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Let $K \subset R^{n} $ be a compact set and $p \in R^m$ then $ \{p \} \times K$ is compact in $R^{n +m}$

Published on 15 Apr 2026 - 22:54

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Quotient space and quotient map

Published on 10 May 2026 - 15:54

280

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Continuity of a function from a one-point compactification to a cone

Published on 10 May 2026 - 14:58

List Question

Closed and bounded but not compact subset of $\ell^1$

Third homotopy group of quotient space

1) Is $\Bbb R \setminus \Bbb Q$ compact? 2) Prove $[0, 1] \times [0, 1]$ and $(0, 1) \times (0, 1)$ are not homeomorphic

How to prove the outer measure of a compact set in Rn is the infimum of sums of volumes of closed cubes?

Erwin kreyszig functional analysis Page.82 Ex.4

is compactness equivalent to limit point compactness?

Definition of relative (sequential) compactness

How to check continuous function $f$ has extension?

Compactness and connectedness of sets

$f$ be real uniformly continuous function on the bounded set $E$ of $\Bbb R$ then $f$ is bounded on $E$

Why we can assume compactness in Victor Klee's theorem?

Unit ball in $l^{2}$ is bounded and closed but not compact.

Let $K \subset R^{n} $ be a compact set and $p \in R^m$ then $ \{p \} \times K$ is compact in $R^{n +m}$

Quotient space and quotient map

Continuity of a function from a one-point compactification to a cone

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