Question

Sequence with distinct points: derived set in the discrete metric

score 444 · Answer 1 · 2018-04-09 10:12:57

444

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Sequence with distinct points: derived set in the discrete metric

Published on 09 Apr 2018 - 10:12

score 86 · Answer 2 · 2026-03-22 18:37:10

86

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Let $S$ be a metric space, $ f: S \to \Bbb R$ continuous. Define $Z(f) = \{p \in S : f(p) = 0 \}$. Prove $Z(f)$ is closed.

Published on 22 Mar 2026 - 18:37

score 549 · Answer 3 · 2018-04-09 19:15:27

549

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Infinite metric on $[-\infty,\infty]$

Published on 09 Apr 2018 - 19:15

score 677 · Answer 4 · 2026-03-25 06:06:21

677

Views

Prove the metric induced topology is the same as the product topology

Published on 25 Mar 2026 - 6:06

score 216 · Answer 5 · 2026-03-25 02:03:05

216

Views

Every conserving metric is Lipschitz equivalent to the euclidean product metric

Published on 25 Mar 2026 - 2:03

score 210 · Answer 6 · 2018-04-10 19:33:32

210

Views

Image of the boundary is equal to the boundary of image.

Published on 10 Apr 2018 - 19:33

score 322 · Answer 7 · 2018-04-10 22:46:03

322

Views

Prove that the set $\{x_n:n\in\mathbb{N}\}\cup\{a\}$ is sequentially compact using sequences

Published on 10 Apr 2018 - 22:46

score 27 · Answer 8 · 2018-04-11 02:27:35

27

Views

A question regarding continuous functions on metric spaces

Published on 11 Apr 2018 - 2:27

score 552 · Answer 9 · 2026-03-25 03:07:13

552

Views

Is subset of convergent sequence bounded?

Published on 25 Mar 2026 - 3:07

score 38 · Answer 10 · 2018-04-11 10:11:16

38

Views

Let $F$ the set of all continuous real functions with domain $[0,a]$. Which of the following are metrics on $F$?

Published on 11 Apr 2018 - 10:11

score 1.2k · Answer 11 · 2018-04-11 12:38:41

1.2k

Views

Relative compact set $M$ admits relative compact $\epsilon$-net in a complete metric space $X$

Published on 11 Apr 2018 - 12:38

score 434 · Answer 12 · 2026-03-25 17:31:04

434

Views

Vanishing at infinity implies uniform continuity

Published on 25 Mar 2026 - 17:31

score 1.1k · Answer 13 · 2018-04-11 18:07:22

1.1k

Views

Relation between homeomorphism and topological equivalence

Published on 11 Apr 2018 - 18:07

score 28 · Answer 14 · 2018-04-11 19:12:09

28

Views

Is the uniform continuity condition required in the following question?

Published on 11 Apr 2018 - 19:12

score 76 · Answer 15 · 2026-03-25 11:53:00

76

Views

Relationship between complete metrics

Published on 25 Mar 2026 - 11:53

List Question

Sequence with distinct points: derived set in the discrete metric

Let $S$ be a metric space, $ f: S \to \Bbb R$ continuous. Define $Z(f) = \{p \in S : f(p) = 0 \}$. Prove $Z(f)$ is closed.

Infinite metric on $[-\infty,\infty]$

Prove the metric induced topology is the same as the product topology

Every conserving metric is Lipschitz equivalent to the euclidean product metric

Image of the boundary is equal to the boundary of image.

Prove that the set $\{x_n:n\in\mathbb{N}\}\cup\{a\}$ is sequentially compact using sequences

A question regarding continuous functions on metric spaces

Is subset of convergent sequence bounded?

Let $F$ the set of all continuous real functions with domain $[0,a]$. Which of the following are metrics on $F$?

Relative compact set $M$ admits relative compact $\epsilon$-net in a complete metric space $X$

Vanishing at infinity implies uniform continuity

Relation between homeomorphism and topological equivalence

Is the uniform continuity condition required in the following question?

Relationship between complete metrics

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