Question

Is a projection f(x,y)=x producing an open set out of an open set, every closed set to a closed set and every compact set to a compact set?

score 192 · Answer 1 · 2026-03-17 12:39:23

192

Views

Is a projection f(x,y)=x producing an open set out of an open set, every closed set to a closed set and every compact set to a compact set?

Published on 17 Mar 2026 - 12:39

score 662 · Answer 2 · 2026-03-23 04:43:33

662

Views

Proving that $P:\mathbb{C}\rightarrow\mathbb{R}$, defined by $P(z)=Re(z)$ is open but is not closed.

Published on 23 Mar 2026 - 4:43

score 723 · Answer 3 · 2026-03-25 08:29:59

723

Views

Restriction of open map on topological space to its subspace is open map

Published on 25 Mar 2026 - 8:29

score 495 · Answer 4 · 2026-03-17 15:34:41

495

Views

A non-continuous function which is open?

Published on 17 Mar 2026 - 15:34

score 915 · Answer 5 · 2026-03-17 09:44:52

915

Views

Image of a closed set is closed under bounded linear transformation between Banach spaces?

Published on 17 Mar 2026 - 9:44

score 119 · Answer 6 · 2026-03-17 05:18:53

119

Views

Bounded inverse (Brezis)

Published on 17 Mar 2026 - 5:18

score 211 · Answer 7 · 2026-03-22 19:06:30

211

Views

Proving a set is open using pre image and continuity of a function

Published on 22 Mar 2026 - 19:06

score 106 · Answer 8 · 2026-03-23 10:59:02

106

Views

Is this an open/ closed set? (Pre image, continuity question)

Published on 23 Mar 2026 - 10:59

score 928 · Answer 9 · 2026-03-25 12:32:50

928

Views

Showing that a harmonic function maps open sets to open sets.

Published on 25 Mar 2026 - 12:32

score 1.9k · Answer 10 · 2026-03-17 10:21:24

1.9k

Views

Is a surjective continuous map with compact domain is open?

Published on 17 Mar 2026 - 10:21

score 950 · Answer 11 · 2026-03-25 09:07:37

950

Views

Canonical projection is open - Projective Space

Published on 25 Mar 2026 - 9:07

score 186 · Answer 12 · 2026-03-22 17:53:35

186

Views

How to show that linear applications are closed and open

Published on 22 Mar 2026 - 17:53

score 86 · Answer 13 · 2026-03-22 18:37:10

86

Views

Let $S$ be a metric space, $ f: S \to \Bbb R$ continuous. Define $Z(f) = \{p \in S : f(p) = 0 \}$. Prove $Z(f)$ is closed.

Published on 22 Mar 2026 - 18:37

score 1.8k · Answer 14 · 2026-03-25 11:37:06

1.8k

Views

Showing the $2$-sphere with antipodal points identified is homeomorphic to the upper hemisphere with antipodal points identified.

Published on 25 Mar 2026 - 11:37

score 552 · Answer 15 · 2026-03-25 12:48:51

552

Views

Function is open iff every element of a subbasis maps to open set?

Published on 25 Mar 2026 - 12:48

List Question

Is a projection f(x,y)=x producing an open set out of an open set, every closed set to a closed set and every compact set to a compact set?

Proving that $P:\mathbb{C}\rightarrow\mathbb{R}$, defined by $P(z)=Re(z)$ is open but is not closed.

Restriction of open map on topological space to its subspace is open map

A non-continuous function which is open?

Image of a closed set is closed under bounded linear transformation between Banach spaces?

Bounded inverse (Brezis)

Proving a set is open using pre image and continuity of a function

Is this an open/ closed set? (Pre image, continuity question)

Showing that a harmonic function maps open sets to open sets.

Is a surjective continuous map with compact domain is open?

Canonical projection is open - Projective Space

How to show that linear applications are closed and open

Let $S$ be a metric space, $ f: S \to \Bbb R$ continuous. Define $Z(f) = \{p \in S : f(p) = 0 \}$. Prove $Z(f)$ is closed.

Showing the $2$-sphere with antipodal points identified is homeomorphic to the upper hemisphere with antipodal points identified.

Function is open iff every element of a subbasis maps to open set?

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