Question

Given two sets, one is closed and contains the other, can I find another closed set that contains one of the sets and is included in the other?

score 37 · Answer 1 · 2018-02-21 17:38:11

Given two sets, one is closed and contains the other, can I find another closed set that contains one of the sets and is included in the other?

score 235 · Answer 2 · 2018-02-21 19:07:11

235

Views

Rudin POMA chapter 4 problem 4

Published on 21 Feb 2018 - 19:07

score 3.8k · Answer 3 · 2018-02-21 20:25:15

3.8k

Views

Show that the union of two topologies need not be a topology.

Published on 21 Feb 2018 - 20:25

score 365 · Answer 4 · 2018-02-21 20:55:45

365

Views

Locally Euclidean property in Topology

Published on 21 Feb 2018 - 20:55

score 66 · Answer 5 · 2018-02-21 22:16:52

66

Views

How can the closure of $(1,7]$ in $(1,7]$ with subspace topology include $7$?

Published on 21 Feb 2018 - 22:16

score 318 · Answer 6 · 2026-03-17 22:02:54

318

Views

Is the closed interval $[0,1]$ always needed to do homotopy?

Published on 17 Mar 2026 - 22:02

score 332 · Answer 7 · 2026-03-27 05:37:41

332

Views

Open and Closed Sets Discrete Metric

Published on 27 Mar 2026 - 5:37

score 871 · Answer 8 · 2018-02-22 05:41:21

871

Views

Showing Closure of Open Interval is the Closed Interval

Published on 22 Feb 2018 - 5:41

score 677 · Answer 9 · 2018-02-22 10:00:49

677

Views

Proving that $U^o=U \setminus \partial{U}$ (Boundary and interior of a set)

Published on 22 Feb 2018 - 10:00

score 499 · Answer 10 · 2018-02-22 13:12:00

499

Views

Why do these two surfaces have the same extrinsic topology?

Published on 22 Feb 2018 - 13:12

score 172 · Answer 11 · 2018-02-22 13:52:33

172

Views

Prove that these statements regarding homeomorphisms are equivalent.

Published on 22 Feb 2018 - 13:52

score 28 · Answer 12 · 2026-03-28 12:14:51

28

Views

Suppose $G,R\subset\mathbb{R}$ are closed sets and $[c_0, d_0]\subset F\cup G$. Show that there exists $l$ such that $\lim c_n=\lim b_n=l$.

Published on 28 Mar 2026 - 12:14

score 884 · Answer 13 · 2018-02-22 14:35:01

884

Views

Show that the space is not locally Euclidean (Topology)

Published on 22 Feb 2018 - 14:35

score 159 · Answer 14 · 2018-02-22 15:13:58

159

Views

Complete metric but not uniformly locally compact on the real line

Published on 22 Feb 2018 - 15:13

score 8.9k · Answer 15 · 2018-02-22 16:56:17

8.9k

Views

Prove that $A$ is dense if and only if any non-empty open set in $X$ has an intersection with $A$

Published on 22 Feb 2018 - 16:56

List Question

Given two sets, one is closed and contains the other, can I find another closed set that contains one of the sets and is included in the other?

Rudin POMA chapter 4 problem 4

Show that the union of two topologies need not be a topology.

Locally Euclidean property in Topology

How can the closure of $(1,7]$ in $(1,7]$ with subspace topology include $7$?

Is the closed interval $[0,1]$ always needed to do homotopy?

Open and Closed Sets Discrete Metric

Showing Closure of Open Interval is the Closed Interval

Proving that $U^o=U \setminus \partial{U}$ (Boundary and interior of a set)

Why do these two surfaces have the same extrinsic topology?

Prove that these statements regarding homeomorphisms are equivalent.

Suppose $G,R\subset\mathbb{R}$ are closed sets and $[c_0, d_0]\subset F\cup G$. Show that there exists $l$ such that $\lim c_n=\lim b_n=l$.

Show that the space is not locally Euclidean (Topology)

Complete metric but not uniformly locally compact on the real line

Prove that $A$ is dense if and only if any non-empty open set in $X$ has an intersection with $A$

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