Question

If $\varphi: A\to X$ is injective and continuous such that $\tilde \varphi: A\to \varphi(A)$ is a homeomorphism, is $\varphi(A)$ open in $X$?

score 60 · Answer 1 · 2026-04-14 11:51:33

If $\varphi: A\to X$ is injective and continuous such that $\tilde \varphi: A\to \varphi(A)$ is a homeomorphism, is $\varphi(A)$ open in $X$?

score 213 · Answer 2 · 2026-04-14 18:19:46

213

Views

Definition of the subbasis : Don't we have to include the empty set?

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score 45 · Answer 3 · 2026-04-10 23:16:54

45

Views

Simple exercise on subspace and product topology

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score 480 · Answer 4 · 2026-04-15 21:16:07

480

Views

Finest topology such that a map is continuous : isn't it the discrete topology?

Published on 15 Apr 2026 - 21:16

score 764 · Answer 5 · 2026-04-16 14:42:36

764

Views

Proving homeomorphism on closed ball

Published on 16 Apr 2026 - 14:42

score 1.8k · Answer 6 · 2026-04-10 14:57:42

1.8k

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Continuous bijection which is not a homeomorphism.

Published on 10 Apr 2026 - 14:57

score 221 · Answer 7 · 2026-04-14 16:59:25

221

Views

Open sets in $\mathbb R\times \mathbb R$ with the dictionary order

Published on 14 Apr 2026 - 16:59

score 35 · Answer 8 · 2026-04-14 04:53:17

35

Views

What is intersection of an $m$-handle and an $n$-manifold in a handle decomposition?

Published on 14 Apr 2026 - 4:53

score 1k · Answer 9 · 2026-04-15 08:58:23

1k

Views

$\{1/2\}\times (1/2,1]$ is not open in the ordered square

Published on 15 Apr 2026 - 8:58

score 444 · Answer 10 · 2026-04-14 21:18:39

444

Views

Munkres, Theorem 16.4

Published on 14 Apr 2026 - 21:18

score 43 · Answer 11 · 2026-04-12 02:10:55

43

Views

Clarification on an exercise from Munkres about a basis for $\mathbb R^2$

Published on 12 Apr 2026 - 2:10

score 2k · Answer 12 · 2026-04-14 22:25:30

2k

Views

Expressing half-open interval [a,b) as infinite intersection of open intervals. (Answer Verification)

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score 78 · Answer 13 · 2026-04-14 14:50:56

78

Views

Quotient map from $GL_2(\Bbb R)$

Published on 14 Apr 2026 - 14:50

score 375 · Answer 14 · 2026-04-11 08:01:40

375

Views

What does it mean for a set to be open inside another set?

Published on 11 Apr 2026 - 8:01

score 111 · Answer 15 · 2026-04-15 07:25:53

111

Views

On separable metric spaces

Published on 15 Apr 2026 - 7:25

List Question

If $\varphi: A\to X$ is injective and continuous such that $\tilde \varphi: A\to \varphi(A)$ is a homeomorphism, is $\varphi(A)$ open in $X$?

Definition of the subbasis : Don't we have to include the empty set?

Simple exercise on subspace and product topology

Finest topology such that a map is continuous : isn't it the discrete topology?

Proving homeomorphism on closed ball

Continuous bijection which is not a homeomorphism.

Open sets in $\mathbb R\times \mathbb R$ with the dictionary order

What is intersection of an $m$-handle and an $n$-manifold in a handle decomposition?

$\{1/2\}\times (1/2,1]$ is not open in the ordered square

Munkres, Theorem 16.4

Clarification on an exercise from Munkres about a basis for $\mathbb R^2$

Expressing half-open interval [a,b) as infinite intersection of open intervals. (Answer Verification)

Quotient map from $GL_2(\Bbb R)$

What does it mean for a set to be open inside another set?

On separable metric spaces

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