Question

Modify the Alexander horned sphere for an embedding $S^2 \hookrightarrow ֓\mathbb{R}^3$ s.t. neither component of $\mathbb{R}^3 − S^2$ is 1-connected.

score 266 · Answer 1 · 2026-04-15 09:03:16

266

Views

Modify the Alexander horned sphere for an embedding $S^2 \hookrightarrow ֓\mathbb{R}^3$ s.t. neither component of $\mathbb{R}^3 − S^2$ is 1-connected.

Published on 15 Apr 2026 - 9:03

score 159 · Answer 2 · 2026-04-11 13:01:37

159

Views

Kuratowski closure-complement question involving unions and intersections

Published on 11 Apr 2026 - 13:01

score 517 · Answer 3 · 2026-04-13 20:19:07

517

Views

Completeness condition for Fréchet space

Published on 13 Apr 2026 - 20:19

score 48 · Answer 4 · 2026-04-14 18:30:15

48

Views

real numbers have the topology with basis, $ [a,b)$ : Determining continuity on general polynomials

Published on 14 Apr 2026 - 18:30

score 22 · Answer 5 · 2026-04-10 07:29:43

22

Views

Properties of $f: X\rightarrow [0,a]^{\omega}$

Published on 10 Apr 2026 - 7:29

score 1k · Answer 6 · 2026-04-13 00:22:36

1k

Views

Problem 1.3.12 from Hatcher

Published on 13 Apr 2026 - 0:22

score 438 · Answer 7 · 2026-04-16 17:19:30

438

Views

Example of an associative function $\mathbb{R}^2 \to \mathbb{R}$ which is continuous in both variables but fails to be continuous

Published on 16 Apr 2026 - 17:19

score 179 · Answer 8 · 2026-05-10 19:35:31

179

Views

A continuum-sized convenient category of topological spaces

Published on 10 May 2026 - 19:35

score 40 · Answer 9 · 2026-04-16 01:38:11

40

Views

ℝ is embedded into $ℝ^d$ via any $ι:ℝ→ℝ^d$ with $ι(x)_1=x$ and ι is related to the projection $ℝ^d$ onto the first coordinate. Does this generalize?

Published on 16 Apr 2026 - 1:38

score 35 · Answer 10 · 2026-04-13 06:44:47

35

Views

Which of the given spaces are homeomorphic?

Published on 13 Apr 2026 - 6:44

score 1.1k · Answer 11 · 2026-04-14 00:23:17

1.1k

Views

Proof of Baby Rudin Theorem 2.43

Published on 14 Apr 2026 - 0:23

score 1.1k · Answer 12 · 2026-05-16 09:08:32

1.1k

Views

Is this proof that a continuous image of a compact metric space is compact correct?

Published on 16 May 2026 - 9:08

score 55 · Answer 13 · 2026-04-16 01:27:09

55

Views

$V_{f,x_1,\cdots,x_n,\epsilon} = \{g\in X:|f(x_i)-g(x_i)|<\epsilon, i=1,\cdots,n\}$ is a topology

Published on 16 Apr 2026 - 1:27

score 41 · Answer 14 · 2026-04-15 01:14:33

41

Views

If $b$ is the largest member of $(X,\leq)$. how does $(a,b]$ become basic open set?

Published on 15 Apr 2026 - 1:14

score 54 · Answer 15 · 2026-04-16 00:44:29

54

Views

Prove that $X\subset Y \Rightarrow \bar{X}\subset \bar{Y}$

Published on 16 Apr 2026 - 0:44

List Question

Modify the Alexander horned sphere for an embedding $S^2 \hookrightarrow ֓\mathbb{R}^3$ s.t. neither component of $\mathbb{R}^3 − S^2$ is 1-connected.

Kuratowski closure-complement question involving unions and intersections

Completeness condition for Fréchet space

real numbers have the topology with basis, $ [a,b)$ : Determining continuity on general polynomials

Properties of $f: X\rightarrow [0,a]^{\omega}$

Problem 1.3.12 from Hatcher

Example of an associative function $\mathbb{R}^2 \to \mathbb{R}$ which is continuous in both variables but fails to be continuous

A continuum-sized convenient category of topological spaces

ℝ is embedded into $ℝ^d$ via any $ι:ℝ→ℝ^d$ with $ι(x)_1=x$ and ι is related to the projection $ℝ^d$ onto the first coordinate. Does this generalize?

Which of the given spaces are homeomorphic?

Proof of Baby Rudin Theorem 2.43

Is this proof that a continuous image of a compact metric space is compact correct?

$V_{f,x_1,\cdots,x_n,\epsilon} = \{g\in X:|f(x_i)-g(x_i)|<\epsilon, i=1,\cdots,n\}$ is a topology

If $b$ is the largest member of $(X,\leq)$. how does $(a,b]$ become basic open set?

Prove that $X\subset Y \Rightarrow \bar{X}\subset \bar{Y}$

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