Question

Closed Sets and Open Sets

score 330 · Answer 1 · 2014-05-22 18:14:43

330

Views

Closed Sets and Open Sets

Published on 22 May 2014 - 18:14

score 770 · Answer 2 · 2026-04-04 11:58:18

770

Views

Why must an interior point of $E$ be an element of $E$?

Published on 04 Apr 2026 - 11:58

score 479 · Answer 3 · 2026-04-13 05:02:48

479

Views

Examples of decreasing sequences of closed sets with constant diameter and empty intersection in complete metric spaces

Published on 13 Apr 2026 - 5:02

score 52 · Answer 4 · 2014-05-24 10:52:35

52

Views

Compatible maps

Published on 24 May 2014 - 10:52

score 419 · Answer 5 · 2026-04-12 22:11:54

419

Views

About interior of the frontier (proof-checking)

Published on 12 Apr 2026 - 22:11

score 33 · Answer 6 · 2014-05-26 07:03:52

33

Views

Counterexample $||S+T||_{\mathbb{B}(E)}<||S||_{\mathbb{B}(E)}+||T||_{\mathbb{B}(E)}$

Published on 26 May 2014 - 7:03

score 260 · Answer 7 · 2026-04-13 02:11:02

260

Views

Equivalent of $\ln\ln(N(\epsilon))$ where $N(\varepsilon)$ is the minimum of balls for covering $A$.

Published on 13 Apr 2026 - 2:11

score 51 · Answer 8 · 2014-05-27 10:37:13

51

Views

Group of distances

Published on 27 May 2014 - 10:37

score 210 · Answer 9 · 2014-05-27 15:59:48

210

Views

Showing a metric space is complete.

Published on 27 May 2014 - 15:59

score 833 · Answer 10 · 2026-03-30 22:00:27

833

Views

Finitely many connected components, prove interiors are also connected

Published on 30 Mar 2026 - 22:00

score 112 · Answer 11 · 2026-04-13 13:27:31

112

Views

Proving that $b \in \overline{A}$ if and only if $\rho(b,A) = 0$

Published on 13 Apr 2026 - 13:27

score 241 · Answer 12 · 2026-04-13 14:03:06

241

Views

A continuous function on the real line such that the preimage of every point is either empty of has exactly 3 points

Published on 13 Apr 2026 - 14:03

score 278 · Answer 13 · 2014-05-29 18:10:44

278

Views

Prove that the distance function $d_p(x,y)=\sum_1^n |x_i-y_i|^p$ $0<p<1$ is a metric on R^n

Published on 29 May 2014 - 18:10

score 6.2k · Answer 14 · 2026-04-09 15:25:44

6.2k

Views

Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous

Published on 09 Apr 2026 - 15:25

score 268 · Answer 15 · 2026-04-13 02:57:29

268

Views

Non-constant Cauchy sequence

Published on 13 Apr 2026 - 2:57

List Question

Closed Sets and Open Sets

Why must an interior point of $E$ be an element of $E$?

Examples of decreasing sequences of closed sets with constant diameter and empty intersection in complete metric spaces

Compatible maps

About interior of the frontier (proof-checking)

Counterexample $||S+T||_{\mathbb{B}(E)}<||S||_{\mathbb{B}(E)}+||T||_{\mathbb{B}(E)}$

Equivalent of $\ln\ln(N(\epsilon))$ where $N(\varepsilon)$ is the minimum of balls for covering $A$.

Group of distances

Showing a metric space is complete.

Finitely many connected components, prove interiors are also connected

Proving that $b \in \overline{A}$ if and only if $\rho(b,A) = 0$

A continuous function on the real line such that the preimage of every point is either empty of has exactly 3 points

Prove that the distance function $d_p(x,y)=\sum_1^n |x_i-y_i|^p$ $0<p<1$ is a metric on R^n

Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous

Non-constant Cauchy sequence

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