Question

Prove $\max \{|x_1 - y_1|,\dots,|x_n - y_n|\}$ is a metric space in $\mathbb{R}^n$

score 1.7k · Answer 1 · 2026-03-27 07:50:41

1.7k

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Prove $\max \{|x_1 - y_1|,\dots,|x_n - y_n|\}$ is a metric space in $\mathbb{R}^n$

Published on 27 Mar 2026 - 7:50

score 42 · Answer 2 · 2018-08-29 02:44:18

42

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Given $X$ enumerable, prove that always exist a metric in which every $p\in X$ is a limit point

Published on 29 Aug 2018 - 2:44

score 1.1k · Answer 3 · 2018-08-29 02:58:36

1.1k

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Cofinite topology on infinite sets can't be induced from a metric space.

Published on 29 Aug 2018 - 2:58

score 78 · Answer 4 · 2018-08-29 16:50:04

78

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If $(X,T)$ and $(Y,T')$ are homemomorphic, and if $T$ is metrizable, does $T'$ metrizable ? Does the metric will be comparable?

Published on 29 Aug 2018 - 16:50

score 315 · Answer 5 · 2018-08-29 17:42:31

315

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If the unit ball is metrizable, are all balls metrizable?

Published on 29 Aug 2018 - 17:42

score 81 · Answer 6 · 2018-08-29 19:17:55

81

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$A\cup A'=A\cup \partial A$

Published on 29 Aug 2018 - 19:17

score 1.4k · Answer 7 · 2026-03-27 07:48:06

1.4k

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Proving $\max (d_1, d_2)$ is a metric

Published on 27 Mar 2026 - 7:48

score 587 · Answer 8 · 2026-03-26 02:46:58

587

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Why does a graph distance have to fulfill the four-point condition?

Published on 26 Mar 2026 - 2:46

score 1.4k · Answer 9 · 2026-03-25 06:03:41

1.4k

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Every finite dimensional normed (real) space is isometrically isomorphic to $\mathbf R^n$

Published on 25 Mar 2026 - 6:03

score 276 · Answer 10 · 2018-08-30 13:42:04

276

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Prove $(R[t],d)$ is an Ultrametric Space

Published on 30 Aug 2018 - 13:42

score 68 · Answer 11 · 2018-08-30 16:09:36

68

Views

$C_{[a,b]} \rightarrow \mathbb{R}$, $x(t) \mapsto f(x) = \int_a^b x(t)dt$ continuous?

Published on 30 Aug 2018 - 16:09

score 52 · Answer 12 · 2018-08-30 18:07:23

52

Views

Continuous Function Defined by a Metric

Published on 30 Aug 2018 - 18:07

score 430 · Answer 13 · 2026-03-26 01:17:25

430

Views

The Distance between two points in a hypothetical universe.

Published on 26 Mar 2026 - 1:17

score 128 · Answer 14 · 2026-03-27 04:56:56

128

Views

Sum of bounded with compact set is totally bounded?

Published on 27 Mar 2026 - 4:56

score 490 · Answer 15 · 2018-08-31 17:37:15

490

Views

Show that the set of bounded real sequences is a metric space with norm defined by $d(x,y)=\sup|x_n-y_n|$.

Published on 31 Aug 2018 - 17:37

List Question

Prove $\max \{|x_1 - y_1|,\dots,|x_n - y_n|\}$ is a metric space in $\mathbb{R}^n$

Given $X$ enumerable, prove that always exist a metric in which every $p\in X$ is a limit point

Cofinite topology on infinite sets can't be induced from a metric space.

If $(X,T)$ and $(Y,T')$ are homemomorphic, and if $T$ is metrizable, does $T'$ metrizable ? Does the metric will be comparable?

If the unit ball is metrizable, are all balls metrizable?

$A\cup A'=A\cup \partial A$

Proving $\max (d_1, d_2)$ is a metric

Why does a graph distance have to fulfill the four-point condition?

Every finite dimensional normed (real) space is isometrically isomorphic to $\mathbf R^n$

Prove $(R[t],d)$ is an Ultrametric Space

$C_{[a,b]} \rightarrow \mathbb{R}$, $x(t) \mapsto f(x) = \int_a^b x(t)dt$ continuous?

Continuous Function Defined by a Metric

The Distance between two points in a hypothetical universe.

Sum of bounded with compact set is totally bounded?

Show that the set of bounded real sequences is a metric space with norm defined by $d(x,y)=\sup|x_n-y_n|$.

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