Question

Why is it sufficient to consider two norms when proving that any norms in finite dimensional metric space is equivalent

score 60 · Answer 1 · 2018-10-20 08:06:55

60

Views

Why is it sufficient to consider two norms when proving that any norms in finite dimensional metric space is equivalent

Published on 20 Oct 2018 - 8:06

score 352 · Answer 2 · 2026-03-25 01:38:05

352

Views

A proof of Hölder's inequality and trying to understand this

Published on 25 Mar 2026 - 1:38

score 47 · Answer 3 · 2026-03-26 06:31:49

47

Views

Is this a natural metric on the space of all unoriented lines in a 2D place with positive slope?

Published on 26 Mar 2026 - 6:31

score 77 · Answer 4 · 2026-03-25 18:08:26

77

Views

$C(\mathbb{R})$ is complete under $d(f,g)= \sum^{\infty}_{k=0} 2^{-k} w(\text{sup}_{[-k,k]} |f(x)-g(x)|)$?

Published on 25 Mar 2026 - 18:08

score 234 · Answer 5 · 2018-10-21 10:37:40

234

Views

What if metric space is replaced by arbitrary topological space, will the result still hold?

Published on 21 Oct 2018 - 10:37

score 504 · Answer 6 · 2026-03-30 22:59:04

504

Views

What is the purpose of differentiating between norms and metrics?

Published on 30 Mar 2026 - 22:59

score 36 · Answer 7 · 2018-10-21 16:16:58

36

Views

WTS in a metric space $X$, $B = \{q \in X | d(p, q)> \delta \}$ is open without using the fact that the complement of a closed set is open

Published on 21 Oct 2018 - 16:16

score 607 · Answer 8 · 2026-03-27 14:52:53

607

Views

Show that if the norms $\| \cdot \|_1$ and $\| \cdot \|_2$ are equivalent, then $(X, \| \cdot \|_1)$ is Banach iff $(X, \| \cdot \|_2)$ is Banach

Published on 27 Mar 2026 - 14:52

score 57 · Answer 9 · 2018-10-21 20:15:36

57

Views

Error in uniform convergence question?

Published on 21 Oct 2018 - 20:15

score 91 · Answer 10 · 2018-10-21 21:50:32

91

Views

Metric Space and Analysis: Prove that if $U$ is an open subset of $\mathbb R$ and $c\in U$, then $U\setminus\{c\}$ is disconnected

Published on 21 Oct 2018 - 21:50

score 304 · Answer 11 · 2018-10-21 22:00:54

304

Views

Can a topology induce a metric?

Published on 21 Oct 2018 - 22:00

score 6.5k · Answer 12 · 2018-10-22 08:01:43

6.5k

Views

Example of a metric space where diameter of a ball is not equal twice the radius

Published on 22 Oct 2018 - 8:01

score 361 · Answer 13 · 2026-03-24 06:26:24

361

Views

Pointwise convergence of average of continuous functions

Published on 24 Mar 2026 - 6:26

score 46 · Answer 14 · 2018-10-22 13:23:23

46

Views

Finding whether a set of continuous functions is open or closed.

Published on 22 Oct 2018 - 13:23

score 144 · Answer 15 · 2018-10-22 15:45:40

144

Views

Determine whether each of the following functions defines a metric on R.

Published on 22 Oct 2018 - 15:45

List Question

Why is it sufficient to consider two norms when proving that any norms in finite dimensional metric space is equivalent

A proof of Hölder's inequality and trying to understand this

Is this a natural metric on the space of all unoriented lines in a 2D place with positive slope?

$C(\mathbb{R})$ is complete under $d(f,g)= \sum^{\infty}_{k=0} 2^{-k} w(\text{sup}_{[-k,k]} |f(x)-g(x)|)$?

What if metric space is replaced by arbitrary topological space, will the result still hold?

What is the purpose of differentiating between norms and metrics?

WTS in a metric space $X$, $B = \{q \in X | d(p, q)> \delta \}$ is open without using the fact that the complement of a closed set is open

Show that if the norms $\| \cdot \|_1$ and $\| \cdot \|_2$ are equivalent, then $(X, \| \cdot \|_1)$ is Banach iff $(X, \| \cdot \|_2)$ is Banach

Error in uniform convergence question?

Metric Space and Analysis: Prove that if $U$ is an open subset of $\mathbb R$ and $c\in U$, then $U\setminus\{c\}$ is disconnected

Can a topology induce a metric?

Example of a metric space where diameter of a ball is not equal twice the radius

Pointwise convergence of average of continuous functions

Finding whether a set of continuous functions is open or closed.

Determine whether each of the following functions defines a metric on R.

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