Question

A Theorem from Munkres' Topology

score 76 · Answer 1 · 2018-06-08 16:14:34

76

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A Theorem from Munkres' Topology

Published on 08 Jun 2018 - 16:14

score 77 · Answer 2 · 2026-03-25 11:20:19

77

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Is the preimage of $f\colon (x_1, x_2) \mapsto x_1+x_2 +x_1x_2$ connected?

Published on 25 Mar 2026 - 11:20

score 236 · Answer 3 · 2026-03-28 15:21:25

236

Views

Connectedness of a subset of structured matrices satisfying prescribed conditions on roots of polynomials

Published on 28 Mar 2026 - 15:21

score 57 · Answer 4 · 2018-06-08 21:36:01

57

Views

Do closed sets with full projections intersect?

Published on 08 Jun 2018 - 21:36

score 831 · Answer 5 · 2026-03-25 05:07:42

831

Views

Is the Trefoil knot isotopic to the unknot (torus) in ambient $\mathbb{R}^4$?

Published on 25 Mar 2026 - 5:07

score 1.5k · Answer 6 · 2026-04-01 23:08:26

1.5k

Views

Every path homotopic to a Piecewise linear path (Hatcher 1.1.4)

Published on 01 Apr 2026 - 23:08

score 216 · Answer 7 · 2026-03-25 09:48:44

216

Views

Does there exist a topological space which is not separable but has the Souslin property?

Published on 25 Mar 2026 - 9:48

score 433 · Answer 8 · 2026-03-25 05:07:43

433

Views

Connecting the definition of ambient isotopy to the intuition

Published on 25 Mar 2026 - 5:07

score 581 · Answer 9 · 2026-03-25 06:28:39

581

Views

kernel of quotient is quotient of kernel?

Published on 25 Mar 2026 - 6:28

score 42 · Answer 10 · 2026-03-25 01:18:30

42

Views

Suppose $A=\bigcup_i A_i$ is f-invariant. Then $f^n(A_i)\subseteq A$ for all $n\in\mathbb{N}$?

Published on 25 Mar 2026 - 1:18

score 2.1k · Answer 11 · 2026-04-01 23:09:17

2.1k

Views

Show that a continuous map $f: S^n \to S^1$ is nullhomotopic.

Published on 01 Apr 2026 - 23:09

score 119 · Answer 12 · 2026-04-02 08:53:48

119

Views

Normal families of uniform covers

Published on 02 Apr 2026 - 8:53

score 1.4k · Answer 13 · 2018-06-09 20:19:22

1.4k

Views

Why are neighborhoods assumed to be open?

Published on 09 Jun 2018 - 20:19

score 122 · Answer 14 · 2018-06-09 21:42:32

122

Views

Let $X$ be a separable Banach space. Let $Y$ be the space formed by adding a point at infinity. Is $Y$ homeomorphic to the unit sphere of $X$?

Published on 09 Jun 2018 - 21:42

score 151 · Answer 15 · 2026-03-25 17:20:05

151

Views

Inconsistency related to the definition of net/directed set in Kelley's General Topology

Published on 25 Mar 2026 - 17:20

List Question

A Theorem from Munkres' Topology

Is the preimage of $f\colon (x_1, x_2) \mapsto x_1+x_2 +x_1x_2$ connected?

Connectedness of a subset of structured matrices satisfying prescribed conditions on roots of polynomials

Do closed sets with full projections intersect?

Is the Trefoil knot isotopic to the unknot (torus) in ambient $\mathbb{R}^4$?

Every path homotopic to a Piecewise linear path (Hatcher 1.1.4)

Does there exist a topological space which is not separable but has the Souslin property?

Connecting the definition of ambient isotopy to the intuition

kernel of quotient is quotient of kernel?

Suppose $A=\bigcup_i A_i$ is f-invariant. Then $f^n(A_i)\subseteq A$ for all $n\in\mathbb{N}$?

Show that a continuous map $f: S^n \to S^1$ is nullhomotopic.

Normal families of uniform covers

Why are neighborhoods assumed to be open?

Let $X$ be a separable Banach space. Let $Y$ be the space formed by adding a point at infinity. Is $Y$ homeomorphic to the unit sphere of $X$?

Inconsistency related to the definition of net/directed set in Kelley's General Topology

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