Question

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

score 751 · Answer 1 · 2026-03-25 11:13:37

751

Views

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

Published on 25 Mar 2026 - 11:13

score 107 · Answer 2 · 2026-04-15 08:35:23

107

Views

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

Published on 15 Apr 2026 - 8:35

score 133 · Answer 3 · 2026-05-11 04:01:59

133

Views

Example of a closed map which is not continuous.

Published on 11 May 2026 - 4:01

score 49 · Answer 4 · 2026-04-13 12:44:35

49

Views

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

Published on 13 Apr 2026 - 12:44

score 118 · Answer 5 · 2026-03-25 12:50:55

118

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 25 Mar 2026 - 12:50

score 80 · Answer 6 · 2026-03-25 15:59:01

80

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 25 Mar 2026 - 15:59

score 18 · Answer 7 · 2026-04-16 06:02:57

18

Views

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

Published on 16 Apr 2026 - 6:02

score 88 · Answer 8 · 2026-04-17 01:00:27

88

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 17 Apr 2026 - 1:00

score 57 · Answer 9 · 2026-04-15 16:05:53

57

Views

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

Published on 15 Apr 2026 - 16:05

score 175 · Answer 10 · 2026-04-16 00:33:00

175

Views

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

Published on 16 Apr 2026 - 0:33

score 60 · Answer 11 · 2026-04-13 06:43:07

60

Views

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

Published on 13 Apr 2026 - 6:43

score 68 · Answer 12 · 2026-03-25 11:11:53

68

Views

An example of an open map that is not closed

Published on 25 Mar 2026 - 11:11

score 289 · Answer 13 · 2026-04-15 22:42:00

289

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 15 Apr 2026 - 22:42

score 336 · Answer 14 · 2026-04-11 18:49:50

336

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 11 Apr 2026 - 18:49

score 3.8k · Answer 15 · 2026-04-10 10:22:40

3.8k

Views

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

Published on 10 Apr 2026 - 10:22

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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