Question

Sequence with distinct points: derived set in the discrete metric

score 447 · Answer 1 · 2026-04-16 02:05:53

447

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Sequence with distinct points: derived set in the discrete metric

Published on 16 Apr 2026 - 2:05

score 92 · Answer 2 · 2026-05-10 12:34:46

92

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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 10 May 2026 - 12:34

score 552 · Answer 3 · 2026-04-13 08:03:26

552

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

Published on 13 Apr 2026 - 8:03

score 680 · Answer 4 · 2026-05-10 14:07:48

680

Views

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

Published on 10 May 2026 - 14:07

score 219 · Answer 5 · 2026-05-11 00:30:40

219

Views

Every conserving metric is Lipschitz equivalent to the euclidean product metric

Published on 11 May 2026 - 0:30

score 213 · Answer 6 · 2026-04-15 19:54:16

213

Views

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

Published on 15 Apr 2026 - 19:54

score 324 · Answer 7 · 2026-04-15 09:36:03

324

Views

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

Published on 15 Apr 2026 - 9:36

score 32 · Answer 8 · 2026-04-17 09:31:26

32

Views

A question regarding continuous functions on metric spaces

Published on 17 Apr 2026 - 9:31

score 555 · Answer 9 · 2026-05-10 16:10:15

555

Views

Is subset of convergent sequence bounded?

Published on 10 May 2026 - 16:10

score 40 · Answer 10 · 2026-04-15 04:49:56

40

Views

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

Published on 15 Apr 2026 - 4:49

score 1.2k · Answer 11 · 2026-04-15 03:44:20

1.2k

Views

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

Published on 15 Apr 2026 - 3:44

score 436 · Answer 12 · 2026-05-10 18:19:51

436

Views

Vanishing at infinity implies uniform continuity

Published on 10 May 2026 - 18:19

score 1.2k · Answer 13 · 2026-04-15 00:15:29

1.2k

Views

Relation between homeomorphism and topological equivalence

Published on 15 Apr 2026 - 0:15

score 31 · Answer 14 · 2026-04-14 17:27:23

31

Views

Is the uniform continuity condition required in the following question?

Published on 14 Apr 2026 - 17:27

score 85 · Answer 15 · 2026-05-10 19:17:50

85

Views

Relationship between complete metrics

Published on 10 May 2026 - 19:17

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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