List questions from closed-map

Published on 22 Jan 2022 - 1:51

127

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An example of a closed quotient map that is not open

Published on 02 Feb 2022 - 15:33

37

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Given domain $[0,T]$, can we have a 2nd order ODE describing $[0,T/2]$...?

Published on 26 Mar 2022 - 17:38

40

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The graph of a linear operator is closed but not continuous (closed graph theorem)

Published on 31 May 2022 - 6:22

54

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Question about continuous but neither open nor closed function on topological space X

Published on 17 Jun 2022 - 9:49

63

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$f: X \rightarrow Y$ injective, closed. Prove that for $U \in \mathcal{T}_x$ and $M$ ⊆ $Y$, ∃ $V \in \mathcal{T}_y$ s.t $M$⊆$V$ and $f^{-1}(V)$ ⊆ $U$

Published on 12 Aug 2022 - 17:01

35

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A question related to the closedness of a map between two topological spaces

Published on 28 Sep 2022 - 14:26

124

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Characterization of Continuous, Closed and Open maps

Published on 28 Oct 2022 - 23:18

237

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Characterizing continuous, open and closed maps via interior and closure operators

Published on 31 Oct 2022 - 1:25

73

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$T-\lambda I$ is closed $\implies (T-\lambda I)^{-1}$ is closed

Published on 03 Nov 2022 - 14:29

22

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Example of closed map from $T_2$-space onto non-$T_2$ quotient?

Published on 05 Dec 2022 - 1:35

51

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Could you suggest a textbook for learning basic properties of spectrum of closed operators?

Published on 22 Dec 2022 - 5:01

40

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$S_1$: compact, $S_2$: any topological space. Then $S_1\times S_2\ni (x,y)\mapsto y\in S_2$ is a closed mapping.

Published on 14 Jan 2023 - 14:30

68

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How can I show that $f\mapsto f'$ is a closed map?

Published on 27 Jan 2023 - 14:07

List Question

How to prove T is a closable operator

An example of a closed quotient map that is not open

Given domain $[0,T]$, can we have a 2nd order ODE describing $[0,T/2]$...?

The graph of a linear operator is closed but not continuous (closed graph theorem)

Question about continuous but neither open nor closed function on topological space X

$f: X \rightarrow Y$ injective, closed. Prove that for $U \in \mathcal{T}_x$ and $M$ ⊆ $Y$, ∃ $V \in \mathcal{T}_y$ s.t $M$⊆$V$ and $f^{-1}(V)$ ⊆ $U$

A question related to the closedness of a map between two topological spaces

Characterization of Continuous, Closed and Open maps

Characterizing continuous, open and closed maps via interior and closure operators

$T-\lambda I$ is closed $\implies (T-\lambda I)^{-1}$ is closed

Example of closed map from $T_2$-space onto non-$T_2$ quotient?

Could you suggest a textbook for learning basic properties of spectrum of closed operators?

$S_1$: compact, $S_2$: any topological space. Then $S_1\times S_2\ni (x,y)\mapsto y\in S_2$ is a closed mapping.

How can I show that $f\mapsto f'$ is a closed map?

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