List questions from metric-spaces

Published on 14 Apr 2026 - 20:25

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Given an example of a metric space in which every sphere has two centers

Published on 12 Apr 2026 - 13:41

697

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Riemannian manifolds are metrizable?

Published on 09 Apr 2026 - 14:31

1.8k

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Does continuity of $f$ imply $f^{-1}(\bar A)\subset\overline{f^{-1}(A)}$?

Published on 15 Apr 2026 - 18:29

489

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Why in open balls is radius $r>0$?

Published on 15 Apr 2026 - 3:56

171

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Prove the equation $\vert d(x,z)-d(y,t)\vert\leq d(x,y)+d(z,t)$

Published on 15 Apr 2026 - 23:36

44

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Why is this set closed?[metric-spaces]

Published on 14 Apr 2026 - 11:30

1k

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Geometry of Metric Spaces

Published on 10 Apr 2026 - 13:21

79

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Easier proof of "countable hypocompactness"

Published on 11 Apr 2026 - 19:10

5.8k

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Prove that square metric on $\mathbb{R}$ is in fact a metric.

Published on 16 Apr 2026 - 8:41

890

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Proving there exist convergent subsequences for bounded sequence of real numbers

Published on 14 Apr 2026 - 11:03

411

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Find continuous $f$ s.t. $f(x,y)^2 = x^2$ ($f: H \to \mathbb{R}$, H connected)

Published on 17 Apr 2026 - 13:53

510

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Gromov hyperbolic metric spaces are quasi-convex

Published on 12 Apr 2026 - 0:29

164

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If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?

Published on 15 Apr 2026 - 4:03

144

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Compactness under different metric?

Published on 13 Apr 2026 - 20:18

List Question

The set of points where two continuous functions agree is closed.

Given an example of a metric space in which every sphere has two centers

Riemannian manifolds are metrizable?

Does continuity of $f$ imply $f^{-1}(\bar A)\subset\overline{f^{-1}(A)}$?

Why in open balls is radius $r>0$?

Prove the equation $\vert d(x,z)-d(y,t)\vert\leq d(x,y)+d(z,t)$

Why is this set closed?[metric-spaces]

Geometry of Metric Spaces

Easier proof of "countable hypocompactness"

Prove that square metric on $\mathbb{R}$ is in fact a metric.

Proving there exist convergent subsequences for bounded sequence of real numbers

Find continuous $f$ s.t. $f(x,y)^2 = x^2$ ($f: H \to \mathbb{R}$, H connected)

Gromov hyperbolic metric spaces are quasi-convex

If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?

Compactness under different metric?

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