List questions from compactness

1.7k

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Prokhorov's Theorem : The Statement. Precompact, Sequentially Compact, Relatively Compact : Definitions.

Published on 23 Apr 2020 - 16:24

494

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Conditions for local isometry to be a symmetric relation.

Published on 26 Mar 2026 - 4:52

127

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Does a small perturbation push the minimizing point of continuous function too far?

Published on 26 Mar 2026 - 11:16

481

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Bijective and continuous map from a compact $T_1$ space onto itself that is not a homemorphism

Published on 03 Apr 2026 - 4:43

166

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Use compactness theorem to prove existence of a Flip-Set

Published on 24 Apr 2020 - 18:06

88

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Check and explain whether X is compact in three topologies provided in the figure.

Published on 24 Apr 2020 - 22:32

50

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Proving $\varphi^{-1}\colon S\to [0,1)$, is not continuous

Published on 25 Apr 2020 - 1:16

50

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Compact set and continue function

Published on 25 Apr 2020 - 17:38

157

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Compact Subset in $C[0,1]$

Published on 24 Feb 2026 - 14:23

88

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Any locally compact space is rim compact

Published on 03 Apr 2026 - 4:39

355

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Verification for Proof of Compactness Theorem

Published on 31 Mar 2026 - 7:49

25

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Does the limit of this function exists in this particular case?

Published on 26 Apr 2020 - 15:37

99

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Closed, Open, Bounded, but not Compact (Proof Verification)

Published on 26 Apr 2020 - 17:32

88

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Prove that $T(E)$ is finite dimensional.

Published on 25 Mar 2026 - 22:09

193

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Prob. 4, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Every compact metrizable space has a countable basis.

Published on 25 Mar 2026 - 10:55

List Question

Prokhorov's Theorem : The Statement. Precompact, Sequentially Compact, Relatively Compact : Definitions.

Conditions for local isometry to be a symmetric relation.

Does a small perturbation push the minimizing point of continuous function too far?

Bijective and continuous map from a compact $T_1$ space onto itself that is not a homemorphism

Use compactness theorem to prove existence of a Flip-Set

Check and explain whether X is compact in three topologies provided in the figure.

Proving $\varphi^{-1}\colon S\to [0,1)$, is not continuous

Compact set and continue function

Compact Subset in $C[0,1]$

Any locally compact space is rim compact

Verification for Proof of Compactness Theorem

Does the limit of this function exists in this particular case?

Closed, Open, Bounded, but not Compact (Proof Verification)

Prove that $T(E)$ is finite dimensional.

Prob. 4, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Every compact metrizable space has a countable basis.

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