Question

Let $S = [0, 1] × [0, 1]$. Which of the following statements are true?

score 55 · Answer 1 · 2018-11-22 22:18:04

55

Views

Let $S = [0, 1] × [0, 1]$. Which of the following statements are true?

Published on 22 Nov 2018 - 22:18

score 2.3k · Answer 2 · 2026-03-25 23:18:49

2.3k

Views

A sequence in $\mathbb{R}$ that has no Cauchy subsequence

Published on 25 Mar 2026 - 23:18

score 521 · Answer 3 · 2018-11-23 10:57:21

521

Views

Show that $d(x, y) = |f (x) − f (y)|$ is a metric on $\mathbb R$

Published on 23 Nov 2018 - 10:57

score 49 · Answer 4 · 2026-03-26 01:01:58

49

Views

Is $T$ bounded if $(X,d)$ is not complete?

Published on 26 Mar 2026 - 1:01

score 438 · Answer 5 · 2018-11-24 02:07:22

438

Views

How to prove the square root of squared metric sum is a metric?

Published on 24 Nov 2018 - 2:07

score 379 · Answer 6 · 2026-03-26 02:44:36

379

Views

Path-conectedness of open balls implies path-connectedness

Published on 26 Mar 2026 - 2:44

score 598 · Answer 7 · 2018-11-24 19:35:14

598

Views

Using Mean Value Theorem to prove $f$ is a contraction

Published on 24 Nov 2018 - 19:35

score 47 · Answer 8 · 2018-11-25 05:11:25

47

Views

Show that $\phi_x(t) = \int_{0}^{t}x(s)ds$ is continuous on $C[0,1]$

Published on 25 Nov 2018 - 5:11

score 127 · Answer 9 · 2018-11-25 05:20:07

127

Views

$f(x)= (f_1(x),f_2(x))$ is continuous on X $\iff $ $f_1$ and $f_2$ are continuous

Published on 25 Nov 2018 - 5:20

score 345 · Answer 10 · 2018-11-25 06:14:17

345

Views

If $(X,d)$ is a metric space, prove that intersection of any collection of compact sets in $(X,d)$ is compact.

Published on 25 Nov 2018 - 6:14

score 668 · Answer 11 · 2018-11-25 06:22:49

668

Views

Prove that a set A is open with respect to metric norm dp if and only if it is open with dq

Published on 25 Nov 2018 - 6:22

score 76 · Answer 12 · 2018-11-25 12:56:18

76

Views

Relatively open subset

Published on 25 Nov 2018 - 12:56

score 51 · Answer 13 · 2018-11-25 22:05:00

51

Views

Characterization of interior in metric spaces

Published on 25 Nov 2018 - 22:05

score 37 · Answer 14 · 2026-03-28 06:08:27

37

Views

Combinining metrics of components into a metric of a complex object - triangular inequality

Published on 28 Mar 2026 - 6:08

score 185 · Answer 15 · 2018-11-26 14:01:40

185

Views

If $C$ is connected subset of a disconnected metric space $X=A\cup B$ then either $C\subseteq A $ or $C \subseteq B$

Published on 26 Nov 2018 - 14:01

List Question

Let $S = [0, 1] × [0, 1]$. Which of the following statements are true?

A sequence in $\mathbb{R}$ that has no Cauchy subsequence

Show that $d(x, y) = |f (x) − f (y)|$ is a metric on $\mathbb R$

Is $T$ bounded if $(X,d)$ is not complete?

How to prove the square root of squared metric sum is a metric?

Path-conectedness of open balls implies path-connectedness

Using Mean Value Theorem to prove $f$ is a contraction

Show that $\phi_x(t) = \int_{0}^{t}x(s)ds$ is continuous on $C[0,1]$

$f(x)= (f_1(x),f_2(x))$ is continuous on X $\iff $ $f_1$ and $f_2$ are continuous

If $(X,d)$ is a metric space, prove that intersection of any collection of compact sets in $(X,d)$ is compact.

Prove that a set A is open with respect to metric norm dp if and only if it is open with dq

Relatively open subset

Characterization of interior in metric spaces

Combinining metrics of components into a metric of a complex object - triangular inequality

If $C$ is connected subset of a disconnected metric space $X=A\cup B$ then either $C\subseteq A $ or $C \subseteq B$

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