List questions from compactness

Published on 24 Dec 2018 - 9:37

732

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Proving every compact space is locally compact.

Published on 24 Dec 2018 - 19:46

114

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Uniform limit points of a sequence of oscillating functions

Published on 23 Feb 2026 - 3:28

3.8k

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Closed subsets of compact sets are compact (original proof)

Published on 25 Dec 2018 - 16:02

467

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

Published on 25 Dec 2018 - 18:52

1k

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

Published on 25 Mar 2026 - 4:57

763

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

Published on 26 Dec 2018 - 20:23

105

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Finite subcover with special property

Published on 26 Dec 2018 - 22:20

363

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

Published on 25 Mar 2026 - 6:24

432

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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 27 Dec 2018 - 12:56

91

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Not necesssarily locally compact and locally compact difference

Published on 27 Dec 2018 - 14:45

1k

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

Published on 28 Dec 2018 - 9:01

152

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Order between compactifications

Published on 28 Dec 2018 - 10:48

600

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

Published on 28 Dec 2018 - 16:25

844

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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 28 Dec 2018 - 19:33

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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