Question

Prob. 7 (b), Sec. 28, in Munkres' TOPOLOGY, 2nd ed: A shrinking self-map of a compact metric space has a unique fixed point

score 1.2k · Answer 1 · 2026-03-25 15:12:14

1.2k

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Prob. 7 (b), Sec. 28, in Munkres' TOPOLOGY, 2nd ed: A shrinking self-map of a compact metric space has a unique fixed point

Published on 25 Mar 2026 - 15:12

score 69 · Answer 2 · 2026-03-25 13:49:06

69

Views

Visualization / sketch for this basic proof about subspace topology

Published on 25 Mar 2026 - 13:49

score 203 · Answer 3 · 2026-03-25 23:56:34

203

Views

Complete metric space on unique metric

Published on 25 Mar 2026 - 23:56

score 45 · Answer 4 · 2019-03-09 11:34:44

45

Views

Closed Sets (Proof help)

Published on 09 Mar 2019 - 11:34

score 272 · Answer 5 · 2026-03-25 23:52:18

272

Views

Proving that the metric space of all sequences of positive integers is complete

Published on 25 Mar 2026 - 23:52

score 56 · Answer 6 · 2026-04-02 01:58:28

56

Views

Show that the function $f$ defined in $l_1$ by $f(x)=\Big(\Big(\sum|x_i|\Big)^2+\sum\frac{1}{2^i}|x_i|^2\Big)^{1/2}$ is a norm equivalent in $l_1$

Published on 02 Apr 2026 - 1:58

score 27 · Answer 7 · 2019-03-10 13:02:32

27

Views

Proof verification: Property of specific continuous map on compact metric space

Published on 10 Mar 2019 - 13:02

score 38 · Answer 8 · 2026-03-25 01:18:26

38

Views

Every finite metric space $X$ can be embedded into $\ell_{C_\epsilon\log(|X|+1)}$ with low distortion

Published on 25 Mar 2026 - 1:18

score 38 · Answer 9 · 2019-03-10 20:02:58

38

Views

Closed sets in metric spaces

Published on 10 Mar 2019 - 20:02

score 335 · Answer 10 · 2019-03-10 20:53:11

335

Views

Interior, exterior, and boundary of deleted neighborhood

Published on 10 Mar 2019 - 20:53

score 123 · Answer 11 · 2026-03-31 07:57:40

123

Views

For $(X,d)$ a compact metric space and $ Y \subsetneq X$ there is no isometry $f:X \to Y$.

Published on 31 Mar 2026 - 7:57

score 126 · Answer 12 · 2026-03-31 05:40:02

126

Views

Bounded metric in compact metric space with continuous function

Published on 31 Mar 2026 - 5:40

score 70 · Answer 13 · 2026-04-06 16:18:01

70

Views

Countable union of closed subsets of $(n,n+1)$

Published on 06 Apr 2026 - 16:18

score 288 · Answer 14 · 2026-03-27 10:09:53

288

Views

Show this induced metric is a metric

Published on 27 Mar 2026 - 10:09

score 164 · Answer 15 · 2019-03-12 04:19:17

164

Views

Uncountable collection of open sets.

Published on 12 Mar 2019 - 4:19

List Question

Prob. 7 (b), Sec. 28, in Munkres' TOPOLOGY, 2nd ed: A shrinking self-map of a compact metric space has a unique fixed point

Visualization / sketch for this basic proof about subspace topology

Complete metric space on unique metric

Closed Sets (Proof help)

Proving that the metric space of all sequences of positive integers is complete

Show that the function $f$ defined in $l_1$ by $f(x)=\Big(\Big(\sum|x_i|\Big)^2+\sum\frac{1}{2^i}|x_i|^2\Big)^{1/2}$ is a norm equivalent in $l_1$

Proof verification: Property of specific continuous map on compact metric space

Every finite metric space $X$ can be embedded into $\ell_{C_\epsilon\log(|X|+1)}$ with low distortion

Closed sets in metric spaces

Interior, exterior, and boundary of deleted neighborhood

For $(X,d)$ a compact metric space and $ Y \subsetneq X$ there is no isometry $f:X \to Y$.

Bounded metric in compact metric space with continuous function

Countable union of closed subsets of $(n,n+1)$

Show this induced metric is a metric

Uncountable collection of open sets.

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