Question

Is there a continuous bijection from open unit interval to open unit disc?

score 328 · Answer 1 · 2026-04-01 12:46:23

328

Views

Is there a continuous bijection from open unit interval to open unit disc?

Published on 01 Apr 2026 - 12:46

score 72 · Answer 2 · 2018-06-20 13:10:53

72

Views

Proof or counterexample related topology of metric spaces

Published on 20 Jun 2018 - 13:10

score 125 · Answer 3 · 2018-06-20 13:15:13

125

Views

Can every basis act as a subbasis?

Published on 20 Jun 2018 - 13:15

score 160 · Answer 4 · 2018-06-20 13:48:02

160

Views

Non-homeomorphicity of $\Bbb{N}$ and $\{0\}\cup\{\frac{1}{n} | n\in \Bbb{N}\} \cup \Bbb{N}$

Published on 20 Jun 2018 - 13:48

score 1.2k · Answer 5 · 2018-06-20 14:17:16

1.2k

Views

Why the collection of all closed sets is not a topology?

Published on 20 Jun 2018 - 14:17

score 475 · Answer 6 · 2026-03-28 15:21:13

What are the connected components of $\Bbb R^2 \setminus \big(\{(x,y) \in \Bbb R^2, x^2+y^2=1\} \cup \{(x,y)\in \Bbb R^2, y=x^2+1\}\big)$?

score 103 · Answer 7 · 2026-03-27 06:16:26

103

Views

What is so special about 1d and 2d?

Published on 27 Mar 2026 - 6:16

score 85 · Answer 8 · 2018-06-20 23:45:09

85

Views

Representation of a closed subset of a second countable set

Published on 20 Jun 2018 - 23:45

score 441 · Answer 9 · 2026-04-02 04:31:48

441

Views

$A \subseteq \mathbb{R}^{2}$ is not homeomorphic to an open subset of $\mathbb{R^{n}}$, $n\geq 3$

Published on 02 Apr 2026 - 4:31

score 2.7k · Answer 10 · 2018-06-21 03:09:00

2.7k

Views

What is the definition of local and global properties and how are they different?

Published on 21 Jun 2018 - 3:09

score 228 · Answer 11 · 2018-06-21 03:49:29

228

Views

A discrete uncountable subset of $\ell^\infty$ in the weak topology

Published on 21 Jun 2018 - 3:49

score 1.7k · Answer 12 · 2018-06-21 09:27:33

1.7k

Views

If every subset in a topological space is closed, prove it is a discrete space

Published on 21 Jun 2018 - 9:27

score 191 · Answer 13 · 2026-03-25 09:27:17

191

Views

Convexity of a convex set minus points close to its frontier.

Published on 25 Mar 2026 - 9:27

score 130 · Answer 14 · 2026-03-24 22:14:07

130

Views

If $f$ is Hölder continuous, are we able to conclude that $(t,x)\mapsto\int_0^tf(x+sh)\:{\rm d}s$ is Hölder continuous?

Published on 24 Mar 2026 - 22:14

score 114 · Answer 15 · 2018-06-21 15:24:35

114

Views

Characterization of discrete topology-like behavior about compact sets.

Published on 21 Jun 2018 - 15:24

List Question

Is there a continuous bijection from open unit interval to open unit disc?

Proof or counterexample related topology of metric spaces

Can every basis act as a subbasis?

Non-homeomorphicity of $\Bbb{N}$ and $\{0\}\cup\{\frac{1}{n} | n\in \Bbb{N}\} \cup \Bbb{N}$

Why the collection of all closed sets is not a topology?

What are the connected components of $\Bbb R^2 \setminus \big(\{(x,y) \in \Bbb R^2, x^2+y^2=1\} \cup \{(x,y)\in \Bbb R^2, y=x^2+1\}\big)$?

What is so special about 1d and 2d?

Representation of a closed subset of a second countable set

$A \subseteq \mathbb{R}^{2}$ is not homeomorphic to an open subset of $\mathbb{R^{n}}$, $n\geq 3$

What is the definition of local and global properties and how are they different?

A discrete uncountable subset of $\ell^\infty$ in the weak topology

If every subset in a topological space is closed, prove it is a discrete space

Convexity of a convex set minus points close to its frontier.

If $f$ is Hölder continuous, are we able to conclude that $(t,x)\mapsto\int_0^tf(x+sh)\:{\rm d}s$ is Hölder continuous?

Characterization of discrete topology-like behavior about compact sets.

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