Question

Proving all 1-dimensional isometries can be expressed as two or less reflections

score 137 · Answer 1 · 2026-03-27 08:42:10

137

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Proving all 1-dimensional isometries can be expressed as two or less reflections

Published on 27 Mar 2026 - 8:42

score 748 · Answer 2 · 2017-04-02 00:30:47

748

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If $f'(x):\mathbb R^n \to \mathbb R^n$ is a isometry, then $f(x)=T(x)+a$.

Published on 02 Apr 2017 - 0:30

score 206 · Answer 3 · 2017-04-03 08:40:48

206

Views

prove metric space X isn't isometric to any subspace of $\Bbb E^n$ for any $n$

Published on 03 Apr 2017 - 8:40

score 81 · Answer 4 · 2017-04-05 19:19:15

81

Views

Geometry Transformations

Published on 05 Apr 2017 - 19:19

score 120 · Answer 5 · 2026-02-23 04:57:45

120

Views

Can a topological embedding of a metric space into a metrizable space be extended to an isometric embedding for some metric on the codomain?

Published on 23 Feb 2026 - 4:57

score 71 · Answer 6 · 2026-02-23 04:56:23

71

Views

Does every metric space that topologically embeds into $\mathbb R^n$ isometrically embeds into some metrizable space homeomorphic to $\mathbb R^n$?

Published on 23 Feb 2026 - 4:56

score 139 · Answer 7 · 2023-01-31 17:03:12

139

Views

Does every semi-orthogonal matrix reduce norms of vectors?

Published on 31 Jan 2023 - 17:03

score 90 · Answer 8 · 2023-02-05 05:38:08

90

Views

Four point graph not embeddable isometrically into any $\mathbb R^n$

Published on 05 Feb 2023 - 5:38

score 183 · Answer 9 · 2023-02-06 18:24:42

183

Views

Euclidean isometry that maps set to subset of itself

Published on 06 Feb 2023 - 18:24

score 30 · Answer 10 · 2023-02-23 06:18:39

30

Views

Isometry of product spaces

Published on 23 Feb 2023 - 6:18

score 110 · Answer 11 · 2026-03-27 03:49:06

110

Views

Show that a vector satisfies some properties after basis change

Published on 27 Mar 2026 - 3:49

score 45 · Answer 12 · 2023-02-27 16:08:29

45

Views

Let $X$ be a compact metric space. If $f:X \to X$ is an isometry, then $f$ is surjective

Published on 27 Feb 2023 - 16:08

score 85 · Answer 13 · 2023-03-03 13:34:22

85

Views

Papa Rudin $4.16$ Lemma

Published on 03 Mar 2023 - 13:34

score 48 · Answer 14 · 2023-03-05 16:07:04

48

Views

Doubt about of isometries representation in $\mathbb{R}^{3}$

Published on 05 Mar 2023 - 16:07

score 463 · Answer 15 · 2023-03-06 15:54:00

463

Views

Proof of Chinese remainder theorem by isomorphism

Published on 06 Mar 2023 - 15:54

List Question

Proving all 1-dimensional isometries can be expressed as two or less reflections

If $f'(x):\mathbb R^n \to \mathbb R^n$ is a isometry, then $f(x)=T(x)+a$.

prove metric space X isn't isometric to any subspace of $\Bbb E^n$ for any $n$

Geometry Transformations

Can a topological embedding of a metric space into a metrizable space be extended to an isometric embedding for some metric on the codomain?

Does every metric space that topologically embeds into $\mathbb R^n$ isometrically embeds into some metrizable space homeomorphic to $\mathbb R^n$?

Does every semi-orthogonal matrix reduce norms of vectors?

Four point graph not embeddable isometrically into any $\mathbb R^n$

Euclidean isometry that maps set to subset of itself

Isometry of product spaces

Show that a vector satisfies some properties after basis change

Let $X$ be a compact metric space. If $f:X \to X$ is an isometry, then $f$ is surjective

Papa Rudin $4.16$ Lemma

Doubt about of isometries representation in $\mathbb{R}^{3}$

Proof of Chinese remainder theorem by isomorphism

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