Question

A linear transformation is open map if and only if surjective and closed map if and only if injective

score 750 · Answer 1 · 2023-04-02 12:30:36

750

Views

A linear transformation is open map if and only if surjective and closed map if and only if injective

Published on 02 Apr 2023 - 12:30

score 104 · Answer 2 · 2023-04-19 21:03:26

104

Views

For a closed subset $F ⊂ X × Y$ , the image $π(F )$ need not be closed in Y

Published on 19 Apr 2023 - 21:03

score 131 · Answer 3 · 2023-05-12 12:22:09

131

Views

Example of a closed map which is not continuous.

Published on 12 May 2023 - 12:22

score 46 · Answer 4 · 2026-02-25 00:47:51

46

Views

A ball in $H^m(\Omega)$ is closed under $L^2$-convergence

Published on 25 Feb 2026 - 0:47

score 117 · Answer 5 · 2023-06-10 08:24:49

117

Views

Let $(X, \mathcal{T})$, $(Y, \mathcal{U})$ be topological spaces, and let $f: X \rightarrow Y$ be a bijection. Then $f$ is open iff $f$ is closed

Published on 10 Jun 2023 - 8:24

score 79 · Answer 6 · 2023-07-17 00:33:52

79

Views

Does there exist a non-continuous clopen function $g: \mathbb R \to \mathbb R$? What about $\mathbb R^n\to \mathbb R^m$?

Published on 17 Jul 2023 - 0:33

score 16 · Answer 7 · 2026-03-09 22:55:11

16

Views

Mappings, Serge Lange Basic mathematics. (f.g)^3 = I

Published on 09 Mar 2026 - 22:55

score 83 · Answer 8 · 2023-10-04 07:46:59

83

Views

How to show directly that the function $f \colon \mathbb{R} \longrightarrow \mathbb{R}$, $x \mapsto x^2$ is a closed map?

Published on 04 Oct 2023 - 7:46

score 54 · Answer 9 · 2023-10-05 16:03:06

54

Views

Is the function $f \colon (0, +\infty) \longrightarrow [-1, 1]$ defined by $f(x) = \sin (1/x)$ a closed map?

Published on 05 Oct 2023 - 16:03

score 172 · Answer 10 · 2023-10-22 09:30:26

172

Views

If $Y$ is a metric space and $f: X \rightarrow Y$ is proper, $f$ is closed

Published on 22 Oct 2023 - 9:30

score 57 · Answer 11 · 2023-12-01 18:46:20

57

Views

General topology question, homeomorphism to a closed subspace of $Y \times K$, $K$ is compact.

Published on 01 Dec 2023 - 18:46

score 67 · Answer 12 · 2024-02-02 09:22:04

67

Views

An example of an open map that is not closed

Published on 02 Feb 2024 - 9:22

score 287 · Answer 13 · 2024-03-07 20:17:19

287

Views

Is it possible too evaluate $\int_0^1 \tan^{-1}\left[\frac{\tanh^{-1}x-\tan^{-1}x}{1+\tanh^{-1}x-\tan^{-1}x}\right]\frac{dx}{x}$? Or numerical result?

Published on 07 Mar 2024 - 20:17

score 333 · Answer 14 · 2015-04-13 11:58:12

333

Views

Does there exist non-compact metric space $X$ such that, any continuous function from $X$ to any Hausdorff space is a closed map?

Published on 13 Apr 2015 - 11:58

score 3.8k · Answer 15 · 2015-06-16 15:55:07

3.8k

Views

Continuous function from a compact space to a Hausdorff space is a closed function

Published on 16 Jun 2015 - 15:55

List Question

A linear transformation is open map if and only if surjective and closed map if and only if injective

For a closed subset $F ⊂ X × Y$ , the image $π(F )$ need not be closed in Y

Example of a closed map which is not continuous.

A ball in $H^m(\Omega)$ is closed under $L^2$-convergence

Let $(X, \mathcal{T})$, $(Y, \mathcal{U})$ be topological spaces, and let $f: X \rightarrow Y$ be a bijection. Then $f$ is open iff $f$ is closed

Does there exist a non-continuous clopen function $g: \mathbb R \to \mathbb R$? What about $\mathbb R^n\to \mathbb R^m$?

Mappings, Serge Lange Basic mathematics. (f.g)^3 = I

How to show directly that the function $f \colon \mathbb{R} \longrightarrow \mathbb{R}$, $x \mapsto x^2$ is a closed map?

Is the function $f \colon (0, +\infty) \longrightarrow [-1, 1]$ defined by $f(x) = \sin (1/x)$ a closed map?

If $Y$ is a metric space and $f: X \rightarrow Y$ is proper, $f$ is closed

General topology question, homeomorphism to a closed subspace of $Y \times K$, $K$ is compact.

An example of an open map that is not closed

Is it possible too evaluate $\int_0^1 \tan^{-1}\left[\frac{\tanh^{-1}x-\tan^{-1}x}{1+\tanh^{-1}x-\tan^{-1}x}\right]\frac{dx}{x}$? Or numerical result?

Does there exist non-compact metric space $X$ such that, any continuous function from $X$ to any Hausdorff space is a closed map?

Continuous function from a compact space to a Hausdorff space is a closed function

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