Question

Find comparable topologies on $X$ and $Y$ such that there exists $f:X⟶Y$ which is continuous or open with respect two but not the others.

score 43 · Answer 1 · 2023-05-16 17:33:52

43

Views

Find comparable topologies on $X$ and $Y$ such that there exists $f:X⟶Y$ which is continuous or open with respect two but not the others.

Published on 16 May 2023 - 17:33

score 86 · Answer 2 · 2023-06-07 17:50:05

86

Views

Open mapping theorem for holomorphic functions from corresponding statement about harmonic functions

Published on 07 Jun 2023 - 17:50

score 118 · Answer 3 · 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 52 · Answer 4 · 2023-07-08 22:30:25

52

Views

Topology Exercise - Solution Verification

Published on 08 Jul 2023 - 22:30

score 31 · Answer 5 · 2023-07-10 19:47:15

31

Views

If $T$ has a continuous inverse, then $R_T$ is closed

Published on 10 Jul 2023 - 19:47

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 118 · Answer 7 · 2023-08-04 16:58:30

118

Views

Does there exist a continuous open map from the closed annulus to the closed disk?

Published on 04 Aug 2023 - 16:58

score 34 · Answer 8 · 2023-09-03 14:59:03

34

Views

Boundedness of Linear Operators on Banach Subspace with Different Norm

Published on 03 Sep 2023 - 14:59

score 101 · Answer 9 · 2023-09-06 19:27:00

101

Views

Is multiplication by a scalar an open map in topological groups?

Published on 06 Sep 2023 - 19:27

score 49 · Answer 10 · 2023-09-14 16:51:11

49

Views

Prove that every $C^1$ submersion is an open mapping.

Published on 14 Sep 2023 - 16:51

score 30 · Answer 11 · 2023-09-26 16:16:32

30

Views

evaluate integral with the kernel of Green function (fundamental solution of Poisson equation) of infinite domain using conformal map

Published on 26 Sep 2023 - 16:16

score 43 · Answer 12 · 2023-10-05 16:20:28

43

Views

Prob. 39, Chap. 7, in Schaum's GENERAL TOPOLOGY: The images of sets of a basis of the domain space under an onto open map ...

Published on 05 Oct 2023 - 16:20

score 76 · Answer 13 · 2023-11-30 04:13:12

76

Views

Is $\mathcal F: L^p(\Bbb R) \to L^q(\Bbb R)$ for $1 < p < 2$ surjective?

Published on 30 Nov 2023 - 4:13

score 67 · Answer 14 · 2023-12-01 17:13:09

67

Views

Proving a natural map is open

Published on 01 Dec 2023 - 17:13

score 33 · Answer 15 · 2024-01-25 04:19:06

33

Views

Open mapping theorem for affine maps between Choquet simplices

Published on 25 Jan 2024 - 4:19

List Question

Find comparable topologies on $X$ and $Y$ such that there exists $f:X⟶Y$ which is continuous or open with respect two but not the others.

Open mapping theorem for holomorphic functions from corresponding statement about harmonic functions

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

Topology Exercise - Solution Verification

If $T$ has a continuous inverse, then $R_T$ is closed

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

Does there exist a continuous open map from the closed annulus to the closed disk?

Boundedness of Linear Operators on Banach Subspace with Different Norm

Is multiplication by a scalar an open map in topological groups?

Prove that every $C^1$ submersion is an open mapping.

evaluate integral with the kernel of Green function (fundamental solution of Poisson equation) of infinite domain using conformal map

Prob. 39, Chap. 7, in Schaum's GENERAL TOPOLOGY: The images of sets of a basis of the domain space under an onto open map ...

Is $\mathcal F: L^p(\Bbb R) \to L^q(\Bbb R)$ for $1 < p < 2$ surjective?

Proving a natural map is open

Open mapping theorem for affine maps between Choquet simplices

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