Question

For what metric spaces $(X, d) \ \exists s > 0$ s.t for all $\epsilon < s$ and all $x \in X$, we have $\text{diam}(B_d(x, \epsilon)) = 2\epsilon$?

score 261 · Answer 1 · 2026-04-16 18:06:49

261

Views

For what metric spaces $(X, d) \ \exists s > 0$ s.t for all $\epsilon < s$ and all $x \in X$, we have $\text{diam}(B_d(x, \epsilon)) = 2\epsilon$?

Published on 16 Apr 2026 - 18:06

score 42 · Answer 2 · 2026-04-14 12:02:29

42

Views

Is construction of countable sequence is sufficient to prove following theorem?

Published on 14 Apr 2026 - 12:02

score 334 · Answer 3 · 2026-04-12 07:32:41

334

Views

Counterexample to make the difference between weakly sequentially compact and sequentially compact explicit

Published on 12 Apr 2026 - 7:32

score 289 · Answer 4 · 2026-04-13 12:25:52

289

Views

Connectedness of the domain in Identity Theorem

Published on 13 Apr 2026 - 12:25

score 550 · Answer 5 · 2026-04-12 19:15:44

550

Views

Threading a two-holed torus which is hanging on a string.

Published on 12 Apr 2026 - 19:15

score 65 · Answer 6 · 2026-04-14 20:27:39

65

Views

Give an example of a set $A$ for which the following sets are pairwise different.

Published on 14 Apr 2026 - 20:27

score 153 · Answer 7 · 2026-05-11 01:01:39

153

Views

$X$ in its one point compactification

Published on 11 May 2026 - 1:01

score 140 · Answer 8 · 2026-04-15 01:37:56

140

Views

Folland Chapter 4 problem 50 (one point compactification)

Published on 15 Apr 2026 - 1:37

score 341 · Answer 9 · 2026-04-15 08:07:51

341

Views

accumulation points of intersection of two open sets

Published on 15 Apr 2026 - 8:07

score 86 · Answer 10 · 2026-04-11 18:30:42

86

Views

Suggestion of books

Published on 11 Apr 2026 - 18:30

score 176 · Answer 11 · 2026-05-10 23:31:34

176

Views

Is the subspace topology of the product topology the initial topology with respect to the restrictions of the projection maps?

Published on 10 May 2026 - 23:31

score 248 · Answer 12 · 2026-04-15 00:38:16

248

Views

Can we rederive the axioms of topology from the structure of the category $\textbf{Top}$?

Published on 15 Apr 2026 - 0:38

score 457 · Answer 13 · 2026-04-13 19:32:26

457

Views

Continuous functions in metric spaces and open sets

Published on 13 Apr 2026 - 19:32

score 396 · Answer 14 · 2026-04-11 10:14:47

396

Views

Two continuous maps agree on an open dense set, must they be equal?

Published on 11 Apr 2026 - 10:14

score 47 · Answer 15 · 2026-04-13 11:29:10

47

Views

open ball such that : $t \mapsto \operatorname{rank}( U+ tA)$ is constant where $^tU U = I_p$

Published on 13 Apr 2026 - 11:29

List Question

For what metric spaces $(X, d) \ \exists s > 0$ s.t for all $\epsilon < s$ and all $x \in X$, we have $\text{diam}(B_d(x, \epsilon)) = 2\epsilon$?

Is construction of countable sequence is sufficient to prove following theorem?

Counterexample to make the difference between weakly sequentially compact and sequentially compact explicit

Connectedness of the domain in Identity Theorem

Threading a two-holed torus which is hanging on a string.

Give an example of a set $A$ for which the following sets are pairwise different.

$X$ in its one point compactification

Folland Chapter 4 problem 50 (one point compactification)

accumulation points of intersection of two open sets

Suggestion of books

Is the subspace topology of the product topology the initial topology with respect to the restrictions of the projection maps?

Can we rederive the axioms of topology from the structure of the category $\textbf{Top}$?

Continuous functions in metric spaces and open sets

Two continuous maps agree on an open dense set, must they be equal?

open ball such that : $t \mapsto \operatorname{rank}( U+ tA)$ is constant where $^tU U = I_p$

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