Question

If $B_n$ is bounded then $\bigcup_{n=0}^{\infty} \varepsilon_n E_n$ is bounded

score 133 · Answer 1 · 2020-07-11 00:35:02

133

Views

If $B_n$ is bounded then $\bigcup_{n=0}^{\infty} \varepsilon_n E_n$ is bounded

Published on 11 Jul 2020 - 0:35

score 838 · Answer 2 · 2016-07-30 10:43:58

838

Views

Show that if a topological space is metrizable then it is so in an infinite number of ways

Published on 30 Jul 2016 - 10:43

score 119 · Answer 3 · 2023-01-31 13:49:58

119

Views

Can a topological embedding of a metric space into a metrizable space be extended to an isometric embedding for some metric on the codomain?

Published on 31 Jan 2023 - 13:49

score 70 · Answer 4 · 2023-01-31 16:19:46

70

Views

Does every metric space that topologically embeds into $\mathbb R^n$ isometrically embeds into some metrizable space homeomorphic to $\mathbb R^n$?

Published on 31 Jan 2023 - 16:19

score 41 · Answer 5 · 2023-03-16 00:39:49

41

Views

How can the implication metrizable -> first countable be generalized?

Published on 16 Mar 2023 - 0:39

score 67 · Answer 6 · 2023-04-14 04:18:08

67

Views

Examples of topological spaces in which the converse of the sequence lemma holds, but is not metrizable

Published on 14 Apr 2023 - 4:18

score 101 · Answer 7 · 2023-04-14 23:12:05

Is there a non-metrizable topological space $X$ for which every closed subset of $X$ is the zero set of a continuous real function on $X$?

score 32 · Answer 8 · 2023-05-25 12:58:30

32

Views

Containment of kernels of continuous seminorms

Published on 25 May 2023 - 12:58

score 45 · Answer 9 · 2023-06-29 20:22:21

45

Views

Applications of Alexandroff-Urysohn metrization theorem

Published on 29 Jun 2023 - 20:22

score 215 · Answer 10 · 2023-07-19 11:40:19

215

Views

Is the difference between metric spaces and ultrametric spaces topological?

Published on 19 Jul 2023 - 11:40

score 45 · Answer 11 · 2023-11-15 19:54:54

45

Views

Show that the following metric is complete on $L_1(X,Y)$

Published on 15 Nov 2023 - 19:54

score 81 · Answer 12 · 2023-11-28 21:35:45

81

Views

Why is ${\mathbb R}^\infty$ with the colimit topology not metrizable?

Published on 28 Nov 2023 - 21:35

score 76 · Answer 13 · 2024-01-04 01:04:35

76

Views

Metrizable topology given by convergence of sequences

Published on 04 Jan 2024 - 1:04

score 47 · Answer 14 · 2024-01-27 00:16:30

47

Views

Locally compact Polish space admits a proper metric

Published on 27 Jan 2024 - 0:16

score 92 · Answer 15 · 2024-02-03 14:58:31

92

Views

If $E$ is the strict inductive limit of Frechet spaces $\lbrace E_k\rbrace$, why can't the countable basis of $E_1$ be appropriated for $E$?

Published on 03 Feb 2024 - 14:58

List Question

If $B_n$ is bounded then $\bigcup_{n=0}^{\infty} \varepsilon_n E_n$ is bounded

Show that if a topological space is metrizable then it is so in an infinite number of ways

Can a topological embedding of a metric space into a metrizable space be extended to an isometric embedding for some metric on the codomain?

Does every metric space that topologically embeds into $\mathbb R^n$ isometrically embeds into some metrizable space homeomorphic to $\mathbb R^n$?

How can the implication metrizable -> first countable be generalized?

Examples of topological spaces in which the converse of the sequence lemma holds, but is not metrizable

Is there a non-metrizable topological space $X$ for which every closed subset of $X$ is the zero set of a continuous real function on $X$?

Containment of kernels of continuous seminorms

Applications of Alexandroff-Urysohn metrization theorem

Is the difference between metric spaces and ultrametric spaces topological?

Show that the following metric is complete on $L_1(X,Y)$

Why is ${\mathbb R}^\infty$ with the colimit topology not metrizable?

Metrizable topology given by convergence of sequences

Locally compact Polish space admits a proper metric

If $E$ is the strict inductive limit of Frechet spaces $\lbrace E_k\rbrace$, why can't the countable basis of $E_1$ be appropriated for $E$?

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