Question

Find continuous functions $f,g$ such that $g\circ f $ is closed and continuous but neither $g$ nor $f$ is closed map.

score 103 · Answer 1 · 2026-03-25 06:22:10

103

Views

Find continuous functions $f,g$ such that $g\circ f $ is closed and continuous but neither $g$ nor $f$ is closed map.

Published on 25 Mar 2026 - 6:22

score 232 · Answer 2 · 2019-01-28 17:17:53

232

Views

Every continuous open mapping from $\mathbb{R}$ into $\mathbb{R}$ is monotonic

Published on 28 Jan 2019 - 17:17

score 984 · Answer 3 · 2019-02-07 17:49:52

984

Views

Motivation: Open Mapping Theorem

Published on 07 Feb 2019 - 17:49

score 23 · Answer 4 · 2019-02-13 13:32:03

23

Views

Show a closed bounded set in $\mathbb{R}^1$ maps to a

Published on 13 Feb 2019 - 13:32

score 133 · Answer 5 · 2019-02-14 09:27:38

133

Views

To show a norm is finer than other norm

Published on 14 Feb 2019 - 9:27

score 773 · Answer 6 · 2019-02-28 16:09:38

773

Views

Does there exist a continuous, open, and surjective map from $f\colon\mathbb{R}^n\to\mathbb{R}^m$ for $m>n$?

Published on 28 Feb 2019 - 16:09

score 526 · Answer 7 · 2019-03-03 22:03:51

526

Views

Saturated subsets of quotient map.

Published on 03 Mar 2019 - 22:03

score 121 · Answer 8 · 2019-03-06 16:35:23

121

Views

Question about the proof open mapping theorem

Published on 06 Mar 2019 - 16:35

score 1.1k · Answer 9 · 2019-04-04 07:13:09

1.1k

Views

Do continuous injections preserve open sets?

Published on 04 Apr 2019 - 7:13

score 519 · Answer 10 · 2019-04-18 20:49:52

519

Views

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

Published on 18 Apr 2019 - 20:49

score 274 · Answer 11 · 2019-04-25 21:32:45

274

Views

The converse of continuous image of a connected set is connected

Published on 25 Apr 2019 - 21:32

score 130 · Answer 12 · 2019-05-04 19:19:00

130

Views

Check whether the map $f(z)={z\over e^z-1}$ is open or not in $\{z|$Im$(z)>0\}$

Published on 04 May 2019 - 19:19

score 152 · Answer 13 · 2019-05-05 09:39:15

152

Views

Want to show an embedding is open if the image is open

Published on 05 May 2019 - 9:39

score 602 · Answer 14 · 2026-03-25 12:54:54

602

Views

Is a differentiable (but not $C^1$) function $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$ with invertible derivative everywhere an open map?

Published on 25 Mar 2026 - 12:54

score 729 · Answer 15 · 2019-06-02 19:27:10

729

Views

Does every linear injective open map between Banach spaces map closed sets to closed sets?

Published on 02 Jun 2019 - 19:27

List Question

Find continuous functions $f,g$ such that $g\circ f $ is closed and continuous but neither $g$ nor $f$ is closed map.

Every continuous open mapping from $\mathbb{R}$ into $\mathbb{R}$ is monotonic

Motivation: Open Mapping Theorem

Show a closed bounded set in $\mathbb{R}^1$ maps to a

To show a norm is finer than other norm

Does there exist a continuous, open, and surjective map from $f\colon\mathbb{R}^n\to\mathbb{R}^m$ for $m>n$?

Saturated subsets of quotient map.

Question about the proof open mapping theorem

Do continuous injections preserve open sets?

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

The converse of continuous image of a connected set is connected

Check whether the map $f(z)={z\over e^z-1}$ is open or not in $\{z|$Im$(z)>0\}$

Want to show an embedding is open if the image is open

Is a differentiable (but not $C^1$) function $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$ with invertible derivative everywhere an open map?

Does every linear injective open map between Banach spaces map closed sets to closed sets?

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