Question

Contact point VS boundary point

score 773 · Answer 1 · 2018-10-26 10:13:55

773

Views

Contact point VS boundary point

Published on 26 Oct 2018 - 10:13

score 125 · Answer 2 · 2018-10-26 13:38:38

125

Views

open singleton metric space

Published on 26 Oct 2018 - 13:38

score 69 · Answer 3 · 2026-03-25 06:27:44

69

Views

Upper bound on distance between trajectories that share same initial position and velocity

Published on 25 Mar 2026 - 6:27

score 29 · Answer 4 · 2026-03-29 08:15:09

29

Views

Open and closed set $X$ which $a\in X$, $b\not\in X$. Then $A$ connected implies $a$ or $b$ not in A

Published on 29 Mar 2026 - 8:15

score 255 · Answer 5 · 2018-10-27 20:40:13

255

Views

Expanding the supremum metric on $C[0,1]$ to $C[a,b]$

Published on 27 Oct 2018 - 20:40

score 79 · Answer 6 · 2026-03-25 21:54:14

79

Views

Proof that in Сauchy metric space the union of a sequence of closed sets with no internal points has no internal points

Published on 25 Mar 2026 - 21:54

score 140 · Answer 7 · 2018-10-28 02:39:41

140

Views

How to prove or disprove the following set is compact?

Published on 28 Oct 2018 - 2:39

score 1.9k · Answer 8 · 2026-03-25 20:10:59

1.9k

Views

Interior and closure of $\mathbb{Q}\cap (0,1)$.

Published on 25 Mar 2026 - 20:10

score 117 · Answer 9 · 2018-10-29 09:52:30

117

Views

Largest distance in an unusual metric

Published on 29 Oct 2018 - 9:52

score 321 · Answer 10 · 2026-03-29 03:10:59

321

Views

Ambiguous definition of a sequence in $l^2$

Published on 29 Mar 2026 - 3:10

score 24 · Answer 11 · 2018-10-30 00:29:30

24

Views

If $\lim_{i\to\infty} x_n^i = x_n$ then $((x_n^i)_{n\in\mathbb{N}})_{i\in\mathbb{N}}\to(x_n)_{n\in\mathbb{N}}$

Published on 30 Oct 2018 - 0:29

score 123 · Answer 12 · 2018-10-30 19:52:23

123

Views

For a discrete metric space in $\mathbb{R}$, $0$ is not a limit point for $\left\{\frac{1}{n}:n\in\mathbb{N}\right\}$.

Published on 30 Oct 2018 - 19:52

score 51 · Answer 13 · 2026-03-25 20:59:50

51

Views

Using the sequence definitions, if $X$ is compact, prove that $X$ is complete

Published on 25 Mar 2026 - 20:59

score 58 · Answer 14 · 2018-10-31 02:00:31

58

Views

$|d(x,A)-d(x,B)|\le d(x,y)$

Published on 31 Oct 2018 - 2:00

score 59 · Answer 15 · 2026-03-31 05:25:33

59

Views

Show that for any real matrix $A$, $||A||_2=\sup_{x\ne0, y\ne 0}\frac{|y^TAx|}{||y||_2||x||_2}$

Published on 31 Mar 2026 - 5:25

List Question

Contact point VS boundary point

open singleton metric space

Upper bound on distance between trajectories that share same initial position and velocity

Open and closed set $X$ which $a\in X$, $b\not\in X$. Then $A$ connected implies $a$ or $b$ not in A

Expanding the supremum metric on $C[0,1]$ to $C[a,b]$

Proof that in Сauchy metric space the union of a sequence of closed sets with no internal points has no internal points

How to prove or disprove the following set is compact?

Interior and closure of $\mathbb{Q}\cap (0,1)$.

Largest distance in an unusual metric

Ambiguous definition of a sequence in $l^2$

If $\lim_{i\to\infty} x_n^i = x_n$ then $((x_n^i)_{n\in\mathbb{N}})_{i\in\mathbb{N}}\to(x_n)_{n\in\mathbb{N}}$

For a discrete metric space in $\mathbb{R}$, $0$ is not a limit point for $\left\{\frac{1}{n}:n\in\mathbb{N}\right\}$.

Using the sequence definitions, if $X$ is compact, prove that $X$ is complete

$|d(x,A)-d(x,B)|\le d(x,y)$

Show that for any real matrix $A$, $||A||_2=\sup_{x\ne0, y\ne 0}\frac{|y^TAx|}{||y||_2||x||_2}$

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