Question

How to recover the tangent space from the metric

score 662 · Answer 1 · 2026-04-03 14:37:15

662

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How to recover the tangent space from the metric

Published on 03 Apr 2026 - 14:37

score 391 · Answer 2 · 2026-03-29 08:18:23

391

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Interior of connected metric spaces are connected?

Published on 29 Mar 2026 - 8:18

score 65 · Answer 3 · 2018-11-01 01:35:29

65

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$d(A,B) \le d(x,A) + d(x,B)$

Published on 01 Nov 2018 - 1:35

score 21 · Answer 4 · 2018-11-01 06:19:35

Show that for each $\delta_1>0$ there is $\delta_2>0$ such that for $x$ in $X$ with $d(x,X’)\ge\delta_1$ we have $d(x,X-\{x\})>\delta_2.$

score 37 · Answer 5 · 2018-11-01 09:51:31

37

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Proof that $C(S)$ is connected for any subset of $\mathbb{R}$

Published on 01 Nov 2018 - 9:51

score 55 · Answer 6 · 2018-11-01 14:15:51

55

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Cauchy criterium

Published on 01 Nov 2018 - 14:15

score 425 · Answer 7 · 2018-11-01 15:52:11

425

Views

If $x$ is an element of the closure of $S$, but not $S$ itself, is it true that there exists a sequence in $S$ with limit $x$?

Published on 01 Nov 2018 - 15:52

score 745 · Answer 8 · 2018-11-02 11:27:57

745

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Prove that if for $E$ and $F$ connected sets, if $E \cap F \neq \emptyset \rightarrow E \cup F$ is connected

Published on 02 Nov 2018 - 11:27

score 213 · Answer 9 · 2018-11-02 17:30:59

213

Views

If $d(x,y)$ is a metric on $X$, then $d'(x,y)=\frac{d(x,y)}{1 + d(x,y)}$ and $d(x,y)$ generates the same topology.

Published on 02 Nov 2018 - 17:30

score 658 · Answer 10 · 2026-03-26 01:01:39

658

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Open connected subsets of path connected spaces

Published on 26 Mar 2026 - 1:01

score 235 · Answer 11 · 2026-03-25 17:26:09

235

Views

Every quasiisometry is a quasiisometric embedding

Published on 25 Mar 2026 - 17:26

score 1.1k · Answer 12 · 2018-11-03 15:30:58

Is $\{ (e^{2\pi i a n},e^{2\pi i b n }) : n \in \mathbb{Z} \}$ dense in the torus, where $a,b$ irrationals such that $a/b$ irrational?

score 189 · Answer 13 · 2026-03-25 19:25:14

189

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Complete space?

Published on 25 Mar 2026 - 19:25

score 352 · Answer 14 · 2026-03-27 16:26:12

352

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how to see that isometries are distance preserving

Published on 27 Mar 2026 - 16:26

score 33 · Answer 15 · 2018-11-04 16:15:30

33

Views

For points $x,y\in\mathbb{R}^{2}$ define $d(x,y)=|(x_{1}-y_{2})^{2}-(x_{2}-y_{1})^{2}|$. Does $d$ define a metric space?

Published on 04 Nov 2018 - 16:15

List Question

How to recover the tangent space from the metric

Interior of connected metric spaces are connected?

$d(A,B) \le d(x,A) + d(x,B)$

Show that for each $\delta_1>0$ there is $\delta_2>0$ such that for $x$ in $X$ with $d(x,X’)\ge\delta_1$ we have $d(x,X-\{x\})>\delta_2.$

Proof that $C(S)$ is connected for any subset of $\mathbb{R}$

Cauchy criterium

If $x$ is an element of the closure of $S$, but not $S$ itself, is it true that there exists a sequence in $S$ with limit $x$?

Prove that if for $E$ and $F$ connected sets, if $E \cap F \neq \emptyset \rightarrow E \cup F$ is connected

If $d(x,y)$ is a metric on $X$, then $d'(x,y)=\frac{d(x,y)}{1 + d(x,y)}$ and $d(x,y)$ generates the same topology.

Open connected subsets of path connected spaces

Every quasiisometry is a quasiisometric embedding

Is $\{ (e^{2\pi i a n},e^{2\pi i b n }) : n \in \mathbb{Z} \}$ dense in the torus, where $a,b$ irrationals such that $a/b$ irrational?

Complete space?

how to see that isometries are distance preserving

For points $x,y\in\mathbb{R}^{2}$ define $d(x,y)=|(x_{1}-y_{2})^{2}-(x_{2}-y_{1})^{2}|$. Does $d$ define a metric space?

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