Question

Denumerable dimensional tvs

score 82 · Answer 1 · 2026-02-23 10:13:41

82

Views

Denumerable dimensional tvs

Published on 23 Feb 2026 - 10:13

score 148 · Answer 2 · 2022-06-08 09:34:02

148

Views

Show that if $u_n:=p(f(x_n),g(y_n))$ for all $n\in \mathbb{N}$, then the sequence $(u_n)$ converges.

Published on 08 Jun 2022 - 9:34

score 28 · Answer 3 · 2022-06-08 17:58:50

28

Views

Show, that $ U = \left\{ u \in W_p^2 (\mathbb{R}_+)\ | \ u(0) = 0 \right\}$ is a closed subspace of $W_p^2 (\mathbb{R}_+)$

Published on 08 Jun 2022 - 17:58

score 38 · Answer 4 · 2022-06-11 02:35:10

38

Views

Show that if $(X,p)$ is complete, then so is $(X,d)$, where $\frac{3}{2022}p(x,y) \le d(x,y) \le \min\{1,p(x,y)\}$, for any $x,y \in X$.

Published on 11 Jun 2022 - 2:35

score 106 · Answer 5 · 2022-06-15 11:04:05

106

Views

To prove completeness in finer topology?

Published on 15 Jun 2022 - 11:04

score 283 · Answer 6 · 2026-03-25 17:37:50

283

Views

Can the surreal numbers be completed to form an ordered field?

Published on 25 Mar 2026 - 17:37

score 44 · Answer 7 · 2022-07-02 07:43:42

44

Views

Confusion about the definition of convergence in metric spaces in Conway's book A Course in Point-set Topology

Published on 02 Jul 2022 - 7:43

score 45 · Answer 8 · 2026-03-25 17:44:05

45

Views

Is $No^2$ or $(\mathbb{R}^*)^2$ rotation invariant?

Published on 25 Mar 2026 - 17:44

score 109 · Answer 9 · 2022-07-12 11:14:47

109

Views

Is a countable union of nested complete metric spaces complete in this case?

Published on 12 Jul 2022 - 11:14

score 143 · Answer 10 · 2026-03-29 10:49:02

143

Views

Neat way to prove that $\mathbb{Q}_p$ is complete via 'field of fractions of inverse limit' definition

Published on 29 Mar 2026 - 10:49

score 65 · Answer 11 · 2026-03-25 22:06:29

65

Views

If the underlying metric is complete, then so is its induced Hausdorff metric

Published on 25 Mar 2026 - 22:06

score 401 · Answer 12 · 2022-08-05 21:50:24

401

Views

Uniqueness of orthogonal projection in closed subspace of Hilbert space

Published on 05 Aug 2022 - 21:50

score 65 · Answer 13 · 2022-08-07 02:26:06

65

Views

A $\sigma$-algebra is complete w.r.t. the metric $d_{\mu}(A, B) := \mu(A \triangle B)$

Published on 07 Aug 2022 - 2:26

score 95 · Answer 14 · 2022-08-11 13:50:56

95

Views

Cc(X) is a Banach algebra iff X is compact

Published on 11 Aug 2022 - 13:50

score 55 · Answer 15 · 2022-08-30 02:41:34

55

Views

A question related to the completion of a complete metric space

Published on 30 Aug 2022 - 2:41

List Question

Denumerable dimensional tvs

Show that if $u_n:=p(f(x_n),g(y_n))$ for all $n\in \mathbb{N}$, then the sequence $(u_n)$ converges.

Show, that $ U = \left\{ u \in W_p^2 (\mathbb{R}_+)\ | \ u(0) = 0 \right\}$ is a closed subspace of $W_p^2 (\mathbb{R}_+)$

Show that if $(X,p)$ is complete, then so is $(X,d)$, where $\frac{3}{2022}p(x,y) \le d(x,y) \le \min\{1,p(x,y)\}$, for any $x,y \in X$.

To prove completeness in finer topology?

Can the surreal numbers be completed to form an ordered field?

Confusion about the definition of convergence in metric spaces in Conway's book A Course in Point-set Topology

Is $No^2$ or $(\mathbb{R}^*)^2$ rotation invariant?

Is a countable union of nested complete metric spaces complete in this case?

Neat way to prove that $\mathbb{Q}_p$ is complete via 'field of fractions of inverse limit' definition

If the underlying metric is complete, then so is its induced Hausdorff metric

Uniqueness of orthogonal projection in closed subspace of Hilbert space

A $\sigma$-algebra is complete w.r.t. the metric $d_{\mu}(A, B) := \mu(A \triangle B)$

Cc(X) is a Banach algebra iff X is compact

A question related to the completion of a complete metric space

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