Question

Prove that a sequence in a set is Cauchy in one metric if it is Cauchy under an equivalent metric

score 71 · Answer 1 · 2026-04-16 08:35:07

71

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Prove that a sequence in a set is Cauchy in one metric if it is Cauchy under an equivalent metric

Published on 16 Apr 2026 - 8:35

score 104 · Answer 2 · 2026-05-11 17:38:19

104

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Completeness of Continuous Functions on Uniform Spaces

Published on 11 May 2026 - 17:38

score 55 · Answer 3 · 2026-05-10 08:22:42

55

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Completeness with distance functions in metric space

Published on 10 May 2026 - 8:22

score 125 · Answer 4 · 2026-04-14 19:06:32

125

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How to show two metrics are isotonic to each other?

Published on 14 Apr 2026 - 19:06

score 770 · Answer 5 · 2026-04-09 08:07:58

770

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Are d1 and lift metric equivalent distances?

Published on 09 Apr 2026 - 8:07

score 372 · Answer 6 · 2026-04-15 23:04:34

372

Views

Show that if $f:M\to\mathbb{R}$ is continuous, $a\in\mathbb{R}$, $\{x:f(x)<a\}$ is an open set in $M$.

Published on 15 Apr 2026 - 23:04

score 238 · Answer 7 · 2026-04-15 05:52:48

238

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Rudin POMA chapter 4 problem 4

Published on 15 Apr 2026 - 5:52

score 69 · Answer 8 · 2026-04-12 10:06:47

69

Views

How can the closure of $(1,7]$ in $(1,7]$ with subspace topology include $7$?

Published on 12 Apr 2026 - 10:06

score 334 · Answer 9 · 2026-04-15 17:49:54

334

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Open and Closed Sets Discrete Metric

Published on 15 Apr 2026 - 17:49

score 175 · Answer 10 · 2026-04-15 15:15:01

175

Views

Prove that these statements regarding homeomorphisms are equivalent.

Published on 15 Apr 2026 - 15:15

score 162 · Answer 11 · 2026-04-12 11:00:50

162

Views

Complete metric but not uniformly locally compact on the real line

Published on 12 Apr 2026 - 11:00

score 8.9k · Answer 12 · 2026-04-14 05:20:59

8.9k

Views

Prove that $A$ is dense if and only if any non-empty open set in $X$ has an intersection with $A$

Published on 14 Apr 2026 - 5:20

score 936 · Answer 13 · 2026-05-10 22:29:17

936

Views

Proving $(X, d)$ is complete if and only if $(X, d')$ is complete

Published on 10 May 2026 - 22:29

score 245 · Answer 14 · 2026-04-15 14:50:49

245

Views

Showing that Closure of a Ball is Not the Closed Ball

Published on 15 Apr 2026 - 14:50

score 2.5k · Answer 15 · 2026-04-09 17:06:49

2.5k

Views

What does it mean if a sequence is not eventually constant

Published on 09 Apr 2026 - 17:06

List Question

Prove that a sequence in a set is Cauchy in one metric if it is Cauchy under an equivalent metric

Completeness of Continuous Functions on Uniform Spaces

Completeness with distance functions in metric space

How to show two metrics are isotonic to each other?

Are d1 and lift metric equivalent distances?

Show that if $f:M\to\mathbb{R}$ is continuous, $a\in\mathbb{R}$, $\{x:f(x)<a\}$ is an open set in $M$.

Rudin POMA chapter 4 problem 4

How can the closure of $(1,7]$ in $(1,7]$ with subspace topology include $7$?

Open and Closed Sets Discrete Metric

Prove that these statements regarding homeomorphisms are equivalent.

Complete metric but not uniformly locally compact on the real line

Prove that $A$ is dense if and only if any non-empty open set in $X$ has an intersection with $A$

Proving $(X, d)$ is complete if and only if $(X, d')$ is complete

Showing that Closure of a Ball is Not the Closed Ball

What does it mean if a sequence is not eventually constant

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