List questions from compactness

Published on 11 Apr 2026 - 20:32

735

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Proving every compact space is locally compact.

Published on 11 Apr 2026 - 12:40

115

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Uniform limit points of a sequence of oscillating functions

Published on 09 Apr 2026 - 8:16

3.8k

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Closed subsets of compact sets are compact (original proof)

Published on 17 Apr 2026 - 8:55

471

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$U\cap K$ is compact in the subspace topology

Published on 15 Apr 2026 - 5:38

1k

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For the existence of one-point compactification, do we need locally compactness?

Published on 10 May 2026 - 17:13

766

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Examine if the following sets are compact in $\mathbb{R^2}$

Published on 11 Apr 2026 - 17:38

108

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Finite subcover with special property

Published on 15 Apr 2026 - 13:44

367

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Does first countable imply equivalence of sequential and limit point compactness?

Published on 10 May 2026 - 19:33

435

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Can anyone give me a example of space which is limit point compact but not compact?(Except the popular sets $S_\Omega$ and $Z \times Y$ )

Published on 14 Apr 2026 - 6:40

94

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Not necesssarily locally compact and locally compact difference

Published on 11 Apr 2026 - 16:44

1k

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Prove that $K$ is a compact set by directly using the definition of compactness.

Published on 11 Apr 2026 - 9:16

155

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Order between compactifications

Published on 10 Apr 2026 - 23:42

603

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A Banach space is $\sigma$-compact iff finite dimensional

Published on 11 Apr 2026 - 16:54

847

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Use the Lebesgue number lemma to prove that $f$ is uniformly continuous if $M$ is compact and $f$ continuous

Published on 12 Apr 2026 - 1:38

List Question

When is $ \overline {T(B)}$ compact?

Proving every compact space is locally compact.

Uniform limit points of a sequence of oscillating functions

Closed subsets of compact sets are compact (original proof)

$U\cap K$ is compact in the subspace topology

For the existence of one-point compactification, do we need locally compactness?

Examine if the following sets are compact in $\mathbb{R^2}$

Finite subcover with special property

Does first countable imply equivalence of sequential and limit point compactness?

Can anyone give me a example of space which is limit point compact but not compact?(Except the popular sets $S_\Omega$ and $Z \times Y$ )

Not necesssarily locally compact and locally compact difference

Prove that $K$ is a compact set by directly using the definition of compactness.

Order between compactifications

A Banach space is $\sigma$-compact iff finite dimensional

Use the Lebesgue number lemma to prove that $f$ is uniformly continuous if $M$ is compact and $f$ continuous

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