List questions from metric-spaces

Published on 21 May 2018 - 13:30

55

Views

Continuity in Metric Space: Closed and Open Sets

Published on 21 May 2018 - 14:25

463

Views

If $X\times Y$ is complete metric space then $X$ and $Y$ are complete metric spaces

Published on 25 Mar 2026 - 13:34

241

Views

Integral Metric on $C([0,1])$

Published on 25 Mar 2026 - 10:58

67

Views

Possible typographical error in Michael Searcoid's book?

Published on 30 Mar 2026 - 6:44

64

Views

Open set in $Q_{p}$ is finite or countable union of open balls?

Published on 25 Mar 2026 - 11:14

108

Views

Let $K\subseteq\mathbb{C}$ be compact and non-empty. Show there exists a $z\in K$ such that $|z|=\inf\{|w|:w\in K\}$.

Published on 28 Mar 2026 - 9:57

439

Views

Equicontinuous family composed with a continuous function

Published on 23 May 2018 - 3:46

23

Views

Prove: $x_n\to p \iff$ Eventually All The Elements Of The Sequence Are In A Neighborhood

Published on 24 May 2018 - 11:29

71

Views

How to understand maps between arbitrary spaces?

Published on 24 May 2018 - 13:30

445

Views

Sequences converges pointwise to $0$ on dense sets

Published on 23 Mar 2026 - 21:44

83

Views

a local property of the distance function on Riemannian manifolds

Published on 25 Mar 2026 - 18:49

135

Views

A vector space inside a metric space inside a vector space

Published on 25 Mar 2026 - 13:32

79

Views

If the set $A$ is open in $X$, is the set $\{x+y : x\in A \}$ also open for a given $y \in X$ under any metric space?

Published on 20 Mar 2026 - 3:26

167

Views

Proving relative compactness of a set on $\ell_{p}$ space

Published on 26 May 2018 - 1:33

List Question

Open set/continuous functions

Continuity in Metric Space: Closed and Open Sets

If $X\times Y$ is complete metric space then $X$ and $Y$ are complete metric spaces

Integral Metric on $C([0,1])$

Possible typographical error in Michael Searcoid's book?

Open set in $Q_{p}$ is finite or countable union of open balls?

Let $K\subseteq\mathbb{C}$ be compact and non-empty. Show there exists a $z\in K$ such that $|z|=\inf\{|w|:w\in K\}$.

Equicontinuous family composed with a continuous function

Prove: $x_n\to p \iff$ Eventually All The Elements Of The Sequence Are In A Neighborhood

How to understand maps between arbitrary spaces?

Sequences converges pointwise to $0$ on dense sets

a local property of the distance function on Riemannian manifolds

A vector space inside a metric space inside a vector space

If the set $A$ is open in $X$, is the set $\{x+y : x\in A \}$ also open for a given $y \in X$ under any metric space?

Proving relative compactness of a set on $\ell_{p}$ space

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