Question

Equivalent definitions of convergence in $\mathbb{R}$ and convergence in $\overline{\mathbb{R}}$

score 103 · Answer 1 · 2019-08-21 05:31:59

103

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Equivalent definitions of convergence in $\mathbb{R}$ and convergence in $\overline{\mathbb{R}}$

Published on 21 Aug 2019 - 5:31

score 170 · Answer 2 · 2026-04-09 02:25:56

170

Views

Inversive geometry: is it possible to point-invert a Euclidean space and not produce a hyperbolic one?

Published on 09 Apr 2026 - 2:25

score 49 · Answer 3 · 2026-03-31 12:52:08

49

Views

reparametrization function

Published on 31 Mar 2026 - 12:52

score 122 · Answer 4 · 2026-03-25 20:51:22

122

Views

Unit sphere difficult isometry

Published on 25 Mar 2026 - 20:51

score 180 · Answer 5 · 2026-03-26 19:37:41

180

Views

compact convergence on a non-compact metric space implies continuity

Published on 26 Mar 2026 - 19:37

score 192 · Answer 6 · 2026-04-08 16:43:37

192

Views

Variations Calculus. How to compute some variations?

Published on 08 Apr 2026 - 16:43

score 99 · Answer 7 · 2019-08-23 01:36:02

Is it possible that a non-empty set has different collections of dense subsets under a (non-trivial) metric and under a (non-trivial) topology?

score 239 · Answer 8 · 2026-03-25 20:53:30

239

Views

Proving that two dimensional hyperbolic space is isometric to the sub-manifold of positive-definite matrices with unit determinant

Published on 25 Mar 2026 - 20:53

score 44 · Answer 9 · 2026-03-25 23:09:02

44

Views

Does their exist a countable $G_\delta$ set in $\Bbb{R}$ with usual metric.

Published on 25 Mar 2026 - 23:09

score 8.1k · Answer 10 · 2026-04-01 11:12:00

8.1k

Views

Compact metric space and convergent subsequence

Published on 01 Apr 2026 - 11:12

score 314 · Answer 11 · 2026-03-26 19:00:37

314

Views

Is the inverse image of a Cauchy sequence of a continuous and injective function a Cauchy sequence?

Published on 26 Mar 2026 - 19:00

score 89 · Answer 12 · 2019-08-25 09:26:04

89

Views

Is X complete with the given metric d.

Published on 25 Aug 2019 - 9:26

score 31 · Answer 13 · 2019-08-26 11:32:53

31

Views

Show a set is open in several variables

Published on 26 Aug 2019 - 11:32

score 148 · Answer 14 · 2026-03-25 19:03:45

148

Views

If a product space is metrisable, are the factor spaces metrisable?

Published on 25 Mar 2026 - 19:03

score 211 · Answer 15 · 2026-03-29 22:14:45

211

Views

$(X,d)$ is a metric space such that every continuous function $f: X \rightarrow \mathbb{R}$ is bounded. Prove $X$ is complete.

Published on 29 Mar 2026 - 22:14

List Question

Equivalent definitions of convergence in $\mathbb{R}$ and convergence in $\overline{\mathbb{R}}$

Inversive geometry: is it possible to point-invert a Euclidean space and not produce a hyperbolic one?

reparametrization function

Unit sphere difficult isometry

compact convergence on a non-compact metric space implies continuity

Variations Calculus. How to compute some variations?

Is it possible that a non-empty set has different collections of dense subsets under a (non-trivial) metric and under a (non-trivial) topology?

Proving that two dimensional hyperbolic space is isometric to the sub-manifold of positive-definite matrices with unit determinant

Does their exist a countable $G_\delta$ set in $\Bbb{R}$ with usual metric.

Compact metric space and convergent subsequence

Is the inverse image of a Cauchy sequence of a continuous and injective function a Cauchy sequence?

Is X complete with the given metric d.

Show a set is open in several variables

If a product space is metrisable, are the factor spaces metrisable?

$(X,d)$ is a metric space such that every continuous function $f: X \rightarrow \mathbb{R}$ is bounded. Prove $X$ is complete.

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