Question

If every infinte subset of E has a limit point in E then E is compact in X

score 666 · Answer 1 · 2018-08-11 11:00:19

666

Views

If every infinte subset of E has a limit point in E then E is compact in X

Published on 11 Aug 2018 - 11:00

score 132 · Answer 2 · 2026-04-01 03:47:53

132

Views

Converse part of triangular inequality hold equality when third point lies in the both point

Published on 01 Apr 2026 - 3:47

score 88 · Answer 3 · 2018-08-11 13:40:21

88

Views

Is the given set open ball in metric space or not?

Published on 11 Aug 2018 - 13:40

score 149 · Answer 4 · 2018-08-12 05:51:14

149

Views

Closed balls in metric space with trivial metric

Published on 12 Aug 2018 - 5:51

score 45 · Answer 5 · 2018-08-12 07:40:05

45

Views

Given $\{(x,y) \in\mathbb{R}^2 | 0 \leq x <1\}$. Show that it is not closed in $(\mathbb{R}^2, \|\cdot\|_2)$

Published on 12 Aug 2018 - 7:40

score 847 · Answer 6 · 2018-08-12 09:31:46

847

Views

every open set in R is the union of an at most countable collection of disjoint segments

Published on 12 Aug 2018 - 9:31

score 97 · Answer 7 · 2026-03-26 02:56:02

97

Views

Prove that $\{x\in \Bbb{R^n} :\;f(x)\leq k\}$ is compact

Published on 26 Mar 2026 - 2:56

score 553 · Answer 8 · 2026-03-26 02:57:52

553

Views

Prove that there exists a continuous function $f:E\to \Bbb{R}$ such that $f(x)=1$ if $x\in A$ and $f(x)=0$ if $x\in B.$

Published on 26 Mar 2026 - 2:57

score 151 · Answer 9 · 2018-08-13 00:15:38

151

Views

On a characterization of quasi-isometric embedding for groups

Published on 13 Aug 2018 - 0:15

score 130 · Answer 10 · 2026-03-29 03:53:18

130

Views

Isn't there any meaning to talk of open spaces, or of closed space?

Published on 29 Mar 2026 - 3:53

score 883 · Answer 11 · 2018-08-13 07:00:46

883

Views

How to visualize the open ball in $C[0,1]$?

Published on 13 Aug 2018 - 7:00

score 3.3k · Answer 12 · 2018-08-13 10:58:17

3.3k

Views

Proof of $cl(A \cup B)=cl(A) \cup cl(B)$

Published on 13 Aug 2018 - 10:58

score 238 · Answer 13 · 2018-08-13 14:32:24

238

Views

Identity function on $C[0,1]$

Published on 13 Aug 2018 - 14:32

score 128 · Answer 14 · 2018-08-13 15:26:40

128

Views

Can any metric on $\Bbb R^n$ be bounded above and below for any other metric?

Published on 13 Aug 2018 - 15:26

score 28 · Answer 15 · 2018-08-14 07:57:26

28

Views

Nontrivial example of closed set relative to subspace but not with respect to original space

Published on 14 Aug 2018 - 7:57

List Question

If every infinte subset of E has a limit point in E then E is compact in X

Converse part of triangular inequality hold equality when third point lies in the both point

Is the given set open ball in metric space or not?

Closed balls in metric space with trivial metric

Given $\{(x,y) \in\mathbb{R}^2 | 0 \leq x <1\}$. Show that it is not closed in $(\mathbb{R}^2, \|\cdot\|_2)$

every open set in R is the union of an at most countable collection of disjoint segments

Prove that $\{x\in \Bbb{R^n} :\;f(x)\leq k\}$ is compact

Prove that there exists a continuous function $f:E\to \Bbb{R}$ such that $f(x)=1$ if $x\in A$ and $f(x)=0$ if $x\in B.$

On a characterization of quasi-isometric embedding for groups

Isn't there any meaning to talk of open spaces, or of closed space?

How to visualize the open ball in $C[0,1]$?

Proof of $cl(A \cup B)=cl(A) \cup cl(B)$

Identity function on $C[0,1]$

Can any metric on $\Bbb R^n$ be bounded above and below for any other metric?

Nontrivial example of closed set relative to subspace but not with respect to original space

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