List questions from metric-spaces

Published on 14 Apr 2019 - 9:03

103

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Verification of proof that $Y$ nowhere dense iff $X\setminus \overline{Y}$ is dense.

Published on 15 Apr 2019 - 0:19

66

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Show that any subspace of a compact space can be covered with one open subspace.

Published on 31 Mar 2026 - 17:53

21

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Count metric induced topologies on countable set.

Published on 15 Apr 2019 - 12:50

168

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A metric on non negative symmetric matrix

Published on 27 Mar 2026 - 7:13

155

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Compactness of a subset of $L_1([0,1])$

Published on 16 Apr 2019 - 16:54

60

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Closedness of the Set of Continuous and Increasing functions

Published on 17 Apr 2019 - 13:19

38

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Compact subset of the image of a continuous function

Published on 17 Apr 2019 - 16:55

1k

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Proof that l2 has a countable and dense subset

Published on 25 Mar 2026 - 14:19

532

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Prove that $\textbf{Int}(Y)$ is the largest open set contained in $Y$

Published on 18 Apr 2019 - 11:45

520

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An isometric mapping $f:(X,d) \to (X, d)$ is an open mapping

Published on 25 Mar 2026 - 19:03

510

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Why coarse maps have to be proper?

Published on 23 Feb 2026 - 2:51

37

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Homeomorphism or not?

Published on 19 Apr 2019 - 17:09

4.6k

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Is set of isolated points of S closed?

Published on 20 Apr 2019 - 12:14

37

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The relationship among different types of fundamental spaces.

Published on 29 Mar 2026 - 4:11

List Question

Prove every subset of in the discrete metric is clopen

Verification of proof that $Y$ nowhere dense iff $X\setminus \overline{Y}$ is dense.

Show that any subspace of a compact space can be covered with one open subspace.

Count metric induced topologies on countable set.

A metric on non negative symmetric matrix

Compactness of a subset of $L_1([0,1])$

Closedness of the Set of Continuous and Increasing functions

Compact subset of the image of a continuous function

Proof that l2 has a countable and dense subset

Prove that $\textbf{Int}(Y)$ is the largest open set contained in $Y$

An isometric mapping $f:(X,d) \to (X, d)$ is an open mapping

Why coarse maps have to be proper?

Homeomorphism or not?

Is set of isolated points of S closed?

The relationship among different types of fundamental spaces.

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