Question

Proof that a singleton set must be closed or open when its ambient space is connected and given subspace is disconnected

score 249 · Answer 1 · 2026-04-14 02:21:25

249

Views

Proof that a singleton set must be closed or open when its ambient space is connected and given subspace is disconnected

Published on 14 Apr 2026 - 2:21

score 51 · Answer 2 · 2026-04-11 11:49:19

51

Views

Proving a set has quotient topology.

Published on 11 Apr 2026 - 11:49

score 75 · Answer 3 · 2026-04-15 11:09:04

75

Views

Existence of one-to-one continuous function from $[0,1]$ to $(0,1)$, from $\Bbb R$ to $[0,1]$, from $\Bbb R$ to $(0,1)$, and from $(0,1]$ to $(0,1)$

Published on 15 Apr 2026 - 11:09

score 901 · Answer 4 · 2026-04-12 14:53:53

901

Views

Cross is not locally Euclidean in Tu Manifolds

Published on 12 Apr 2026 - 14:53

score 53 · Answer 5 · 2026-04-12 20:13:01

53

Views

What does it mean to say that a topology is defined by a metric?

Published on 12 Apr 2026 - 20:13

score 109 · Answer 6 · 2026-04-08 16:21:01

109

Views

Distinguish the homeomorphism from the imbedding in the definition of locally Euclidean in Tu Manifolds

Published on 08 Apr 2026 - 16:21

score 76 · Answer 7 · 2026-04-16 13:17:15

76

Views

Uniqueness In Proof For Fundamental Group Of $S^1$

Published on 16 Apr 2026 - 13:17

score 682 · Answer 8 · 2026-04-14 16:35:03

682

Views

Dimension of topological manifold and dimension of smooth manifold in Tu Manifolds

Published on 14 Apr 2026 - 16:35

score 3.6k · Answer 9 · 2026-04-14 20:41:51

3.6k

Views

Manifolds of zero dimension and $\mathbb R^0$?

Published on 14 Apr 2026 - 20:41

score 88 · Answer 10 · 2026-04-10 21:12:17

88

Views

Continuous bijection equivalent to homeomorphism under suitable hypotheses

Published on 10 Apr 2026 - 21:12

score 374 · Answer 11 · 2026-04-08 19:06:12

374

Views

Is every continious image of a non-compact space is non-compact?

Published on 08 Apr 2026 - 19:06

score 65 · Answer 12 · 2026-04-28 12:06:59

65

Views

Given set U is first countable or not?

Published on 28 Apr 2026 - 12:06

score 109 · Answer 13 · 2026-04-14 07:17:48

109

Views

$\mathbb{R} \times \mathbb{R} \times ... \times \mathbb{R}$ ($n$ times) is homeomorphic to $\mathbb{R}^{n}$

Published on 14 Apr 2026 - 7:17

score 219 · Answer 14 · 2026-04-14 03:50:49

219

Views

Topology induced by the Euclidean metric

Published on 14 Apr 2026 - 3:50

score 111 · Answer 15 · 2026-04-14 14:53:17

111

Views

Let $E \subset \mathbb{R}^n$ be a convex set. Prove there exists an open set $A \subset \mathbb{R}^n$ equivalent to $E$

Published on 14 Apr 2026 - 14:53

List Question

Proof that a singleton set must be closed or open when its ambient space is connected and given subspace is disconnected

Proving a set has quotient topology.

Existence of one-to-one continuous function from $[0,1]$ to $(0,1)$, from $\Bbb R$ to $[0,1]$, from $\Bbb R$ to $(0,1)$, and from $(0,1]$ to $(0,1)$

Cross is not locally Euclidean in Tu Manifolds

What does it mean to say that a topology is defined by a metric?

Distinguish the homeomorphism from the imbedding in the definition of locally Euclidean in Tu Manifolds

Uniqueness In Proof For Fundamental Group Of $S^1$

Dimension of topological manifold and dimension of smooth manifold in Tu Manifolds

Manifolds of zero dimension and $\mathbb R^0$?

Continuous bijection equivalent to homeomorphism under suitable hypotheses

Is every continious image of a non-compact space is non-compact?

Given set U is first countable or not?

$\mathbb{R} \times \mathbb{R} \times ... \times \mathbb{R}$ ($n$ times) is homeomorphic to $\mathbb{R}^{n}$

Topology induced by the Euclidean metric

Let $E \subset \mathbb{R}^n$ be a convex set. Prove there exists an open set $A \subset \mathbb{R}^n$ equivalent to $E$

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