Question

Does every metric satisfy translation invariance property $d(x+a,y+a)=d(x,y)$

score 1.8k · Answer 1 · 2026-04-15 06:57:32

1.8k

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Does every metric satisfy translation invariance property $d(x+a,y+a)=d(x,y)$

Published on 15 Apr 2026 - 6:57

score 2.7k · Answer 2 · 2026-04-16 13:58:11

2.7k

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If a compact set is covered by a finite union of open balls of same radii, can we always get a lesser radius?

Published on 16 Apr 2026 - 13:58

score 77 · Answer 3 · 2026-05-11 00:48:15

77

Views

Assuring Lipschitzian and contraction of a mapping

Published on 11 May 2026 - 0:48

score 123 · Answer 4 · 2026-04-15 09:14:36

$x \in \overline{A}$ with respect to the topology induced by a metric iff there exists a sequence of points in $A$ that converge to $x$.

score 121 · Answer 5 · 2026-04-15 06:02:59

121

Views

Show that on any uncountable set $X$, there is a metric on $X$ with respect to which $X$ is not separable

Published on 15 Apr 2026 - 6:02

score 82 · Answer 6 · 2026-05-01 01:09:29

82

Views

A metric for capturing "fairness"

Published on 01 May 2026 - 1:09

score 101 · Answer 7 · 2026-05-11 10:15:11

101

Views

Is there a name for the concept of adding "wind" to a metric space?

Published on 11 May 2026 - 10:15

score 101 · Answer 8 · 2026-04-15 00:05:42

Let $(M,d)$ be a metric space. Prove that $A \subset M$ is closed iff whenever every disk about $x$ meets $A$ then $x \in A.$

score 133 · Answer 9 · 2026-05-10 20:56:32

133

Views

Infinite dimensional analysis

Published on 10 May 2026 - 20:56

score 1.4k · Answer 10 · 2026-05-07 10:33:42

1.4k

Views

An injective continuous map between two compact Hausdorff spaces.

Published on 07 May 2026 - 10:33

score 1.3k · Answer 11 · 2026-04-11 02:16:44

1.3k

Views

Unsure how to prove that this function is homeomorphism:

Published on 11 Apr 2026 - 2:16

score 181 · Answer 12 · 2026-05-10 14:56:03

181

Views

The metrics $d_1, d_2$ induce the same topology on $X$

Published on 10 May 2026 - 14:56

score 320 · Answer 13 · 2026-04-13 19:08:51

320

Views

Topological spaces and metric spaces - notion of open sets

Published on 13 Apr 2026 - 19:08

score 1.2k · Answer 14 · 2026-04-12 23:47:38

1.2k

Views

Is the continuous image of a complete metric space complete?

Published on 12 Apr 2026 - 23:47

score 3.6k · Answer 15 · 2026-05-10 14:04:56

3.6k

Views

Proof maximum number of equidistant points for a given dimension

Published on 10 May 2026 - 14:04

List Question

Does every metric satisfy translation invariance property $d(x+a,y+a)=d(x,y)$

If a compact set is covered by a finite union of open balls of same radii, can we always get a lesser radius?

Assuring Lipschitzian and contraction of a mapping

$x \in \overline{A}$ with respect to the topology induced by a metric iff there exists a sequence of points in $A$ that converge to $x$.

Show that on any uncountable set $X$, there is a metric on $X$ with respect to which $X$ is not separable

A metric for capturing "fairness"

Is there a name for the concept of adding "wind" to a metric space?

Let $(M,d)$ be a metric space. Prove that $A \subset M$ is closed iff whenever every disk about $x$ meets $A$ then $x \in A.$

Infinite dimensional analysis

An injective continuous map between two compact Hausdorff spaces.

Unsure how to prove that this function is homeomorphism:

The metrics $d_1, d_2$ induce the same topology on $X$

Topological spaces and metric spaces - notion of open sets

Is the continuous image of a complete metric space complete?

Proof maximum number of equidistant points for a given dimension

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