Question

Is every separable locally compact metrizable topology induced by a Heine-Borel metric?

score 136 · Answer 1 · 2026-03-25 11:23:38

136

Views

Is every separable locally compact metrizable topology induced by a Heine-Borel metric?

Published on 25 Mar 2026 - 11:23

score 683 · Answer 2 · 2018-12-20 18:39:29

683

Views

If $f: \mathbb{R} \to \mathbb{R}$ is a continuous surjection, must it be open?

Published on 20 Dec 2018 - 18:39

score 24 · Answer 3 · 2018-12-20 19:03:05

($\cal{T}$ be the collection of open subsets, $\cal{K}$ the collection of closed subsets). There is a bijection from $\cal{T}$ to $\cal{K}$

score 63 · Answer 4 · 2018-12-20 20:45:52

63

Views

$\bigcup U_{i}$ and $\bigcup V_{j}$ are homeomorphic iff there are equally many $U_{i}$ and $V_{j}$ where $U_{i},V_{i}$ are open.

Published on 20 Dec 2018 - 20:45

score 168 · Answer 5 · 2018-12-20 21:21:41

168

Views

The boundary of $r$-neighborhood of $p$ is not equal to sphere of radius $r$ at $p$

Published on 20 Dec 2018 - 21:21

score 148 · Answer 6 · 2026-03-26 14:40:40

148

Views

Frobenius norm induced distances between distribution inputs

Published on 26 Mar 2026 - 14:40

score 1.3k · Answer 7 · 2018-12-21 03:45:34

1.3k

Views

Identity map between metric spaces continuous or not.

Published on 21 Dec 2018 - 3:45

score 92 · Answer 8 · 2026-02-23 01:05:13

92

Views

Is every uniformity for a metrizable topology metrizable?

Published on 23 Feb 2026 - 1:05

score 740 · Answer 9 · 2018-12-21 17:00:49

740

Views

Equivalent statements about a metric space (homeomorphism, continuity, cluster points, clopen sets and compacts)

Published on 21 Dec 2018 - 17:00

score 23 · Answer 10 · 2026-03-25 22:25:58

23

Views

Choosing a correct option related to compactness and completeness about image of map.

Published on 25 Mar 2026 - 22:25

score 63 · Answer 11 · 2026-03-30 05:30:11

63

Views

There is $a_{0} \in A$, $b_{0} \in B$ such that $d(a_{0},b_{0}) \leq d(a,b)$ if $A,B$ are compacts

Published on 30 Mar 2026 - 5:30

score 98 · Answer 12 · 2018-12-22 02:56:41

98

Views

Is it necessary that either $f(x) \leq 0$ for all $x$, or, $f(x) \geq 0$ for all $x$

Published on 22 Dec 2018 - 2:56

score 569 · Answer 13 · 2026-03-29 13:27:46

569

Views

The interior of a disconnected set is disconnected?

Published on 29 Mar 2026 - 13:27

score 127 · Answer 14 · 2026-02-23 01:07:31

127

Views

Is every uniformizable topology induced by a Heine-Borel uniformity?

Published on 23 Feb 2026 - 1:07

score 195 · Answer 15 · 2026-03-29 13:29:03

195

Views

If $f: M \to \mathbb{R}$ is a continuous function such that all values are irrationals, then $f$ is constant whenever $M$ is connected?

Published on 29 Mar 2026 - 13:29

List Question

Is every separable locally compact metrizable topology induced by a Heine-Borel metric?

If $f: \mathbb{R} \to \mathbb{R}$ is a continuous surjection, must it be open?

($\cal{T}$ be the collection of open subsets, $\cal{K}$ the collection of closed subsets). There is a bijection from $\cal{T}$ to $\cal{K}$

$\bigcup U_{i}$ and $\bigcup V_{j}$ are homeomorphic iff there are equally many $U_{i}$ and $V_{j}$ where $U_{i},V_{i}$ are open.

The boundary of $r$-neighborhood of $p$ is not equal to sphere of radius $r$ at $p$

Frobenius norm induced distances between distribution inputs

Identity map between metric spaces continuous or not.

Is every uniformity for a metrizable topology metrizable?

Equivalent statements about a metric space (homeomorphism, continuity, cluster points, clopen sets and compacts)

Choosing a correct option related to compactness and completeness about image of map.

There is $a_{0} \in A$, $b_{0} \in B$ such that $d(a_{0},b_{0}) \leq d(a,b)$ if $A,B$ are compacts

Is it necessary that either $f(x) \leq 0$ for all $x$, or, $f(x) \geq 0$ for all $x$

The interior of a disconnected set is disconnected?

Is every uniformizable topology induced by a Heine-Borel uniformity?

If $f: M \to \mathbb{R}$ is a continuous function such that all values are irrationals, then $f$ is constant whenever $M$ is connected?

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