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 233 · Answer 2 · 2026-03-25 23:36:26

233

Views

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

Published on 25 Mar 2026 - 23:36

score 986 · Answer 3 · 2026-04-10 18:43:07

986

Views

Motivation: Open Mapping Theorem

Published on 10 Apr 2026 - 18:43

score 24 · Answer 4 · 2026-03-25 23:37:29

24

Views

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

Published on 25 Mar 2026 - 23:37

score 134 · Answer 5 · 2026-03-25 23:38:43

134

Views

To show a norm is finer than other norm

Published on 25 Mar 2026 - 23:38

score 774 · Answer 6 · 2026-03-25 20:42:08

774

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 25 Mar 2026 - 20:42

score 527 · Answer 7 · 2026-03-25 19:02:05

527

Views

Saturated subsets of quotient map.

Published on 25 Mar 2026 - 19:02

score 122 · Answer 8 · 2026-03-25 20:32:30

122

Views

Question about the proof open mapping theorem

Published on 25 Mar 2026 - 20:32

score 1.1k · Answer 9 · 2026-03-25 20:32:30

1.1k

Views

Do continuous injections preserve open sets?

Published on 25 Mar 2026 - 20:32

score 520 · Answer 10 · 2026-03-25 19:03:52

520

Views

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

Published on 25 Mar 2026 - 19:03

score 275 · Answer 11 · 2026-03-25 23:38:40

275

Views

The converse of continuous image of a connected set is connected

Published on 25 Mar 2026 - 23:38

score 131 · Answer 12 · 2026-03-25 19:06:25

131

Views

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

Published on 25 Mar 2026 - 19:06

score 153 · Answer 13 · 2026-03-25 22:11:15

153

Views

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

Published on 25 Mar 2026 - 22:11

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 730 · Answer 15 · 2026-03-25 22:09:30

730

Views

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

Published on 25 Mar 2026 - 22:09

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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