Question

Nagata-Smirnov vs. Urysohn metrization theorems - an example?

score 243 · Answer 1 · 2019-07-17 09:40:47

243

Views

Nagata-Smirnov vs. Urysohn metrization theorems - an example?

Published on 17 Jul 2019 - 9:40

score 235 · Answer 2 · 2014-11-16 21:11:07

235

Views

Metrizability of intersection of two topologies

Published on 16 Nov 2014 - 21:11

score 137 · Answer 3 · 2019-12-10 11:55:12

137

Views

What qualifies as a "separation axiom?"

Published on 10 Dec 2019 - 11:55

score 758 · Answer 4 · 2019-12-11 10:42:35

758

Views

Metric spaces are metrizable?

Published on 11 Dec 2019 - 10:42

score 250 · Answer 5 · 2020-02-05 02:12:56

250

Views

Is a totally ordered, separable and connected topological space metrizable (in the order topology)?

Published on 05 Feb 2020 - 2:12

score 415 · Answer 6 · 2020-02-05 09:11:07

415

Views

Monotone convergence theorem for sequences in a completely metrizable totally ordered topological space

Published on 05 Feb 2020 - 9:11

score 114 · Answer 7 · 2020-02-05 13:58:10

114

Views

In a totally ordered topological space that is connected and metrizable, does every sequence have a monotone subsequence?

Published on 05 Feb 2020 - 13:58

score 180 · Answer 8 · 2020-03-22 13:13:29

180

Views

Is the topology on compact connected Lie groups metrizable?

Published on 22 Mar 2020 - 13:13

score 1.3k · Answer 9 · 2020-04-08 20:33:22

1.3k

Views

A topology that is finer than a metrizable topology is also metrizable?

Published on 08 Apr 2020 - 20:33

score 345 · Answer 10 · 2020-04-28 16:00:16

345

Views

Prob. 6, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: $\mathbb{R}_\ell$ and $I_0^2$ are not metrizable

Published on 28 Apr 2020 - 16:00

score 236 · Answer 11 · 2020-05-22 21:25:19

236

Views

Show that if $X$ is compact metrizable then $C(X)$ is separable.

Published on 22 May 2020 - 21:25

score 59 · Answer 12 · 2020-05-26 11:19:26

$(\prod_{i\in I}X_i, \mathcal{T}_p)$ is metrizable iff $X_i$ is metrizable and all $X_i$ is singleton set except countable many indices.

score 67 · Answer 13 · 2020-06-10 16:05:32

67

Views

Why the open-ball topology functor from $\boldsymbol{Met_c}$ to $\boldsymbol{Top_m}$ is not an isomorphism? Are they isomorphic at all?

Published on 10 Jun 2020 - 16:05

score 39 · Answer 14 · 2020-06-23 17:15:36

39

Views

In a metrizable TVS $E$ a point $x$ is an accumulation point of a sequence $S$ if and only if $S$ contains a subsequence which converges to $x$.

Published on 23 Jun 2020 - 17:15

score 359 · Answer 15 · 2020-06-29 18:22:52

359

Views

The countable product of Fréchet spaces is a Fréchet space

Published on 29 Jun 2020 - 18:22

List Question

Nagata-Smirnov vs. Urysohn metrization theorems - an example?

Metrizability of intersection of two topologies

What qualifies as a "separation axiom?"

Metric spaces are metrizable?

Is a totally ordered, separable and connected topological space metrizable (in the order topology)?

Monotone convergence theorem for sequences in a completely metrizable totally ordered topological space

In a totally ordered topological space that is connected and metrizable, does every sequence have a monotone subsequence?

Is the topology on compact connected Lie groups metrizable?

A topology that is finer than a metrizable topology is also metrizable?

Prob. 6, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: $\mathbb{R}_\ell$ and $I_0^2$ are not metrizable

Show that if $X$ is compact metrizable then $C(X)$ is separable.

$(\prod_{i\in I}X_i, \mathcal{T}_p)$ is metrizable iff $X_i$ is metrizable and all $X_i$ is singleton set except countable many indices.

Why the open-ball topology functor from $\boldsymbol{Met_c}$ to $\boldsymbol{Top_m}$ is not an isomorphism? Are they isomorphic at all?

In a metrizable TVS $E$ a point $x$ is an accumulation point of a sequence $S$ if and only if $S$ contains a subsequence which converges to $x$.

The countable product of Fréchet spaces is a Fréchet space

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