List questions from open-map

Published on 30 Jan 2024 - 14:39

68

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An example of an open map that is not closed

Published on 25 Mar 2026 - 11:11

135

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Prove a mapping is open

Published on 14 Mar 2026 - 10:12

39

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Non-surjective linear operator that is open?

Published on 28 Feb 2024 - 17:40

28

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continuous open mapping of segment

Published on 09 Mar 2024 - 9:36

50

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Proving the set of surjective bounded linear operators is open in Banach space

Published on 24 Mar 2024 - 6:41

5.5k

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When is the quotient space of a second countable space second countable?

Published on 25 Mar 2026 - 17:26

6.2k

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continuous image of a locally compact space is locally compact

Published on 18 May 2015 - 3:36

22k

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A bijective continuous map is a homeomorphism iff it is open, or equivalently, iff it is closed.

Published on 25 Mar 2026 - 22:03

1.2k

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Let $Y$ be a finite-dimensional normed space, $X$ a normed space, and $T: X \to Y$ a surjective linear operator. Show that $T$ is an open mapping.

Published on 02 Oct 2015 - 8:34

987

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Are meromorphic functions open?

Published on 25 Mar 2026 - 18:50

614

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Discontinuous surjective linear map which is not open

Published on 14 Dec 2015 - 12:19

172

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$f:\mathbb R^2 \to \mathbb R$ be a function , $|f(x)-f(y)|\ge 3\|x-y\| , \forall x,y \in \mathbb R^2$ ; is $f(\mathbb R^2)$ open in $\mathbb R$?

Published on 09 May 2016 - 3:58

382

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Proving these equivalent conditions for an open map using boundary of a set

Published on 06 Mar 2026 - 9:54

62

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Proving the set $E(f) = \{(x,y,z)\in\mathbb{R}^3 \ | \ z > f(x,y) \}$ is open if $f$ is continuous.

Published on 22 Jun 2016 - 12:35

List Question

Counterexample of Open Mapping Theorem

An example of an open map that is not closed

Prove a mapping is open

Non-surjective linear operator that is open?

continuous open mapping of segment

Proving the set of surjective bounded linear operators is open in Banach space

When is the quotient space of a second countable space second countable?

continuous image of a locally compact space is locally compact

A bijective continuous map is a homeomorphism iff it is open, or equivalently, iff it is closed.

Let $Y$ be a finite-dimensional normed space, $X$ a normed space, and $T: X \to Y$ a surjective linear operator. Show that $T$ is an open mapping.

Are meromorphic functions open?

Discontinuous surjective linear map which is not open

$f:\mathbb R^2 \to \mathbb R$ be a function , $|f(x)-f(y)|\ge 3\|x-y\| , \forall x,y \in \mathbb R^2$ ; is $f(\mathbb R^2)$ open in $\mathbb R$?

Proving these equivalent conditions for an open map using boundary of a set

Proving the set $E(f) = \{(x,y,z)\in\mathbb{R}^3 \ | \ z > f(x,y) \}$ is open if $f$ is continuous.

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