Question

What shape is homeomorphic to a sphere attached with a handle and a cross cap?

score 809 · Answer 1 · 2026-03-25 15:41:37

809

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What shape is homeomorphic to a sphere attached with a handle and a cross cap?

Published on 25 Mar 2026 - 15:41

score 458 · Answer 2 · 2018-06-24 07:24:02

458

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Let $f : X \rightarrow f(X)$ be continuous and X connected. Then $f(X)$ is connected.

Published on 24 Jun 2018 - 7:24

score 536 · Answer 3 · 2018-06-24 07:44:52

536

Views

{0,1} is not a retract of [0.1]

Published on 24 Jun 2018 - 7:44

score 185 · Answer 4 · 2026-04-06 02:17:26

185

Views

Different definitions of proper actions

Published on 06 Apr 2026 - 2:17

score 114 · Answer 5 · 2018-06-24 21:25:57

114

Views

Prove sum of line segments with ending points included with euclidean metric is complete iff compact

Published on 24 Jun 2018 - 21:25

score 289 · Answer 6 · 2026-03-29 13:40:33

289

Views

Proving open set is equivalent across normed spaces

Published on 29 Mar 2026 - 13:40

score 541 · Answer 7 · 2018-06-24 22:37:58

541

Views

If $K\subset{\mathbb{R}}$ closed and bounded, then K compact Proof (without covers)

Published on 24 Jun 2018 - 22:37

score 1.9k · Answer 8 · 2026-03-25 22:11:05

1.9k

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Why does the concept of differentiation have the meaning only on open sets?

Published on 25 Mar 2026 - 22:11

score 210 · Answer 9 · 2026-03-25 06:32:04

210

Views

What is the explicit equivalence relation for an adjunction space $X\cup_f Y$

Published on 25 Mar 2026 - 6:32

score 63 · Answer 10 · 2018-06-25 05:14:36

63

Views

Let $A \subseteq S \subseteq \mathbb{R}^n$. Show that $A$ is connected in $S$ if and only if $A$ is connected in $\mathbb{R}^n$

Published on 25 Jun 2018 - 5:14

score 617 · Answer 11 · 2026-02-23 04:38:30

617

Views

Topology induced by equivalent norms

Published on 23 Feb 2026 - 4:38

score 416 · Answer 12 · 2018-06-25 10:58:48

416

Views

Prove there is no continous bijection $f:(0,1)\to S^1$ nor $g:[0,1]\to S^1$

Published on 25 Jun 2018 - 10:58

score 23 · Answer 13 · 2018-06-25 11:12:17

Finding a homeomorphismus between $\big(X=\mathbb{R}^2,\mathcal{T}(d_2)\big)$, $\big(Y=(-1,1)\times(-1,1), \mathcal{T} (d_2 \vert_{Y \times Y})\big)$

score 117 · Answer 14 · 2026-03-25 22:41:28

117

Views

Linear functionals continuos on the unit ball with respect to SOT implies it is continuous with respect to WOT on the unit ball

Published on 25 Mar 2026 - 22:41

score 261 · Answer 15 · 2018-06-25 17:28:30

261

Views

Dense and nowhere dense

Published on 25 Jun 2018 - 17:28

List Question

What shape is homeomorphic to a sphere attached with a handle and a cross cap?

Let $f : X \rightarrow f(X)$ be continuous and X connected. Then $f(X)$ is connected.

{0,1} is not a retract of [0.1]

Different definitions of proper actions

Prove sum of line segments with ending points included with euclidean metric is complete iff compact

Proving open set is equivalent across normed spaces

If $K\subset{\mathbb{R}}$ closed and bounded, then K compact Proof (without covers)

Why does the concept of differentiation have the meaning only on open sets?

What is the explicit equivalence relation for an adjunction space $X\cup_f Y$

Let $A \subseteq S \subseteq \mathbb{R}^n$. Show that $A$ is connected in $S$ if and only if $A$ is connected in $\mathbb{R}^n$

Topology induced by equivalent norms

Prove there is no continous bijection $f:(0,1)\to S^1$ nor $g:[0,1]\to S^1$

Finding a homeomorphismus between $\big(X=\mathbb{R}^2,\mathcal{T}(d_2)\big)$, $\big(Y=(-1,1)\times(-1,1), \mathcal{T} (d_2 \vert_{Y \times Y})\big)$

Linear functionals continuos on the unit ball with respect to SOT implies it is continuous with respect to WOT on the unit ball

Dense and nowhere dense

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