Question

uniformly discrete in one metric but not in the other giving the same topology

score 22 · Answer 1 · 2018-09-04 18:43:53

22

Views

uniformly discrete in one metric but not in the other giving the same topology

Published on 04 Sep 2018 - 18:43

score 410 · Answer 2 · 2018-09-05 03:40:03

410

Views

Whether $(C[0,1],d_1)$ is separable or not

Published on 05 Sep 2018 - 3:40

score 203 · Answer 3 · 2018-09-05 06:06:37

203

Views

Prove that $q(x,y)=(\sum\limits_{i=1}^nd_i(x_i,y_i)^2)^{\frac{1}{2}}$ is a metric.

Published on 05 Sep 2018 - 6:06

score 841 · Answer 4 · 2018-09-05 09:18:11

841

Views

Metric Given by Riemann integral

Published on 05 Sep 2018 - 9:18

score 220 · Answer 5 · 2018-09-05 15:28:53

220

Views

“Area metric” and “Hausdorff metric” are not equivalent on all closed polygons, but equivalent on convex closed polygons

Published on 05 Sep 2018 - 15:28

score 828 · Answer 6 · 2018-09-05 23:11:12

828

Views

Every convergent sequence $(x_n)$ is bounded in $(M,d)$

Published on 05 Sep 2018 - 23:11

score 82 · Answer 7 · 2018-09-06 04:54:56

82

Views

Distance between closed and open balls in a normed vector space

Published on 06 Sep 2018 - 4:54

score 240 · Answer 8 · 2018-09-06 08:39:54

240

Views

Show that if $f|_{F_1}$ and $f|_{F_2}$ are continuous function so $f$ continuous on $A$

Published on 06 Sep 2018 - 8:39

score 217 · Answer 9 · 2026-03-26 06:27:12

217

Views

Angles in CAT$(\kappa)$ spaces

Published on 26 Mar 2026 - 6:27

score 97 · Answer 10 · 2026-03-26 09:26:59

97

Views

Metric on the space $\lbrace (u,v) \in \mathbb{R}^3\times\mathbb{R}^3 , \langle u,v\rangle=0 \rbrace$

Published on 26 Mar 2026 - 9:26

score 208 · Answer 11 · 2018-09-06 19:21:38

208

Views

How to connect the definitions of open sets and continuous functions w.r.t. metric space and topological space?

Published on 06 Sep 2018 - 19:21

score 491 · Answer 12 · 2018-09-07 04:21:24

491

Views

If a set and its complement both have empty interior, then the boundary of each of them is $X$

Published on 07 Sep 2018 - 4:21

score 198 · Answer 13 · 2026-03-25 08:56:11

198

Views

Some questions about Hausdorff distance

Published on 25 Mar 2026 - 8:56

score 58 · Answer 14 · 2026-03-30 12:43:43

58

Views

Prove that a sequence of vectors $(x^{(k)})$, where $x^{(k)} = (x^{(k)}_1,...,x^{(k)}_n)$, converges to $x = (x_1,...,x_n)$

Published on 30 Mar 2026 - 12:43

score 90 · Answer 15 · 2018-09-07 22:05:19

90

Views

Prove that triangle inequality holds for $d(x,y) = \frac{|x-y|}{1+|x-y|}$

Published on 07 Sep 2018 - 22:05

List Question

uniformly discrete in one metric but not in the other giving the same topology

Whether $(C[0,1],d_1)$ is separable or not

Prove that $q(x,y)=(\sum\limits_{i=1}^nd_i(x_i,y_i)^2)^{\frac{1}{2}}$ is a metric.

Metric Given by Riemann integral

“Area metric” and “Hausdorff metric” are not equivalent on all closed polygons, but equivalent on convex closed polygons

Every convergent sequence $(x_n)$ is bounded in $(M,d)$

Distance between closed and open balls in a normed vector space

Show that if $f|_{F_1}$ and $f|_{F_2}$ are continuous function so $f$ continuous on $A$

Angles in CAT$(\kappa)$ spaces

Metric on the space $\lbrace (u,v) \in \mathbb{R}^3\times\mathbb{R}^3 , \langle u,v\rangle=0 \rbrace$

How to connect the definitions of open sets and continuous functions w.r.t. metric space and topological space?

If a set and its complement both have empty interior, then the boundary of each of them is $X$

Some questions about Hausdorff distance

Prove that a sequence of vectors $(x^{(k)})$, where $x^{(k)} = (x^{(k)}_1,...,x^{(k)}_n)$, converges to $x = (x_1,...,x_n)$

Prove that triangle inequality holds for $d(x,y) = \frac{|x-y|}{1+|x-y|}$

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