Question

Prove that for an open and continuous map $f:X \to Y$ between topological spaces, it is $f(\tau_X)=\tau_Y$

score 553 · Answer 1 · 2017-02-17 14:24:05

553

Views

Prove that for an open and continuous map $f:X \to Y$ between topological spaces, it is $f(\tau_X)=\tau_Y$

Published on 17 Feb 2017 - 14:24

score 342 · Answer 2 · 2017-02-23 18:39:57

342

Views

Is a faithfully flat map of affine schemes open?

Published on 23 Feb 2017 - 18:39

score 52 · Answer 3 · 2017-02-25 07:47:42

52

Views

$f$ is open iff $f(U)$ is open for every $U$ open set of a fixed point $x \in X$ in a homogeneous space

Published on 25 Feb 2017 - 7:47

score 79 · Answer 4 · 2017-03-02 13:40:24

79

Views

Does there exist an open map satisfying the following properties which is continuous?

Published on 02 Mar 2017 - 13:40

score 154 · Answer 5 · 2017-03-04 13:29:54

154

Views

Incorrect proof of the Open Mapping Theorem

Published on 04 Mar 2017 - 13:29

score 200 · Answer 6 · 2026-03-25 23:36:31

200

Views

Is convex-hull operation an open mapping?

Published on 25 Mar 2026 - 23:36

score 43 · Answer 7 · 2026-03-26 04:53:24

43

Views

Showing $\forall q\in\mathcal{P}_Y$ there exists $ p\in\mathcal{P}_X:q\circ A\le p\implies A:X\to Y$ continuous

Published on 26 Mar 2026 - 4:53

score 340 · Answer 8 · 2017-03-18 23:02:15

340

Views

Why does an open map send generic points to generic point?

Published on 18 Mar 2017 - 23:02

score 476 · Answer 9 · 2017-03-26 08:50:19

476

Views

Why is the inverse of a bounded bijective operator continuous?

Published on 26 Mar 2017 - 8:50

score 640 · Answer 10 · 2017-03-30 18:47:04

640

Views

Is exponentiation open?

Published on 30 Mar 2017 - 18:47

score 35 · Answer 11 · 2023-02-10 19:37:48

35

Views

Topology generated by maps and subbase

Published on 10 Feb 2023 - 19:37

score 185 · Answer 12 · 2023-02-26 05:33:19

185

Views

$f$ is open iff the image of the unit ball contains a ball centered at 0

Published on 26 Feb 2023 - 5:33

score 192 · Answer 13 · 2023-03-19 09:26:58

192

Views

Open mapping theorem for Frechet spaces

Published on 19 Mar 2023 - 9:26

score 64 · Answer 14 · 2026-02-23 02:42:16

64

Views

Why aren't all surjective continuous homomorphisms of topological groups open?

Published on 23 Feb 2026 - 2:42

score 751 · Answer 15 · 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

List Question

Prove that for an open and continuous map $f:X \to Y$ between topological spaces, it is $f(\tau_X)=\tau_Y$

Is a faithfully flat map of affine schemes open?

$f$ is open iff $f(U)$ is open for every $U$ open set of a fixed point $x \in X$ in a homogeneous space

Does there exist an open map satisfying the following properties which is continuous?

Incorrect proof of the Open Mapping Theorem

Is convex-hull operation an open mapping?

Showing $\forall q\in\mathcal{P}_Y$ there exists $ p\in\mathcal{P}_X:q\circ A\le p\implies A:X\to Y$ continuous

Why does an open map send generic points to generic point?

Why is the inverse of a bounded bijective operator continuous?

Is exponentiation open?

Topology generated by maps and subbase

$f$ is open iff the image of the unit ball contains a ball centered at 0

Open mapping theorem for Frechet spaces

Why aren't all surjective continuous homomorphisms of topological groups open?

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

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