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Understanding a statement about equivalent norms ($||\cdot ||_2 \sim||\cdot||_1 $)

score 423 · Answer 1 · 2026-04-14 14:38:01

423

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Understanding a statement about equivalent norms ($||\cdot ||_2 \sim||\cdot||_1 $)

Published on 14 Apr 2026 - 14:38

score 1.6k · Answer 2 · 2026-04-15 18:20:02

1.6k

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Definition of CAT(0) metric space

Published on 15 Apr 2026 - 18:20

score 77 · Answer 3 · 2026-04-13 04:08:47

77

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Interior of a Dirichlet domain in a Riemannian manifold

Published on 13 Apr 2026 - 4:08

score 41 · Answer 4 · 2026-04-10 01:38:13

41

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metric-spaces closure

Published on 10 Apr 2026 - 1:38

score 107 · Answer 5 · 2026-04-14 06:42:33

107

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We know that a Compact set is closed. However a finite discreet set is compact but not closed (contradicting the theorem?)

Published on 14 Apr 2026 - 6:42

score 99 · Answer 6 · 2026-04-15 09:36:38

99

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prove that there is maximum and minimum for C[0,1]

Published on 15 Apr 2026 - 9:36

score 85 · Answer 7 · 2026-04-12 13:24:09

85

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Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?

Published on 12 Apr 2026 - 13:24

score 190 · Answer 8 · 2026-04-17 01:31:32

190

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Show that for any subsets $A,B\subset X$: (i):$d(A\bigcup B)\leq d(A)+d(B)+d(A,B)$ and (ii) $d(\bar A)=d(A)$

Published on 17 Apr 2026 - 1:31

score 1.8k · Answer 9 · 2026-04-09 06:44:35

1.8k

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Does a (local) uniqueness theorem exist for geodesics in metric spaces?

Published on 09 Apr 2026 - 6:44

score 2k · Answer 10 · 2026-04-16 12:34:14

2k

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Definition of disc and open ball

Published on 16 Apr 2026 - 12:34

score 481 · Answer 11 · 2026-04-14 05:44:33

481

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Lipschitz continuous set-valued map

Published on 14 Apr 2026 - 5:44

score 1.9k · Answer 12 · 2026-03-25 03:00:41

1.9k

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Defining the integral on an arbitrary metric space

Published on 25 Mar 2026 - 3:00

score 147 · Answer 13 · 2026-04-16 04:56:27

d' is finer than d on compact space $\implies$ $\forall \epsilon \ \ \exists \epsilon' \ \ \forall x \ B_{d'}(x,\epsilon') \subseteq B_d(x,\epsilon)$

score 64 · Answer 14 · 2026-04-14 21:48:28

64

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Finsler Metric from page 2 of the book by Chern and Shen.

Published on 14 Apr 2026 - 21:48

score 209 · Answer 15 · 2026-04-11 00:32:38

209

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Isometry fixing an open set pointwise is identity

Published on 11 Apr 2026 - 0:32

List Question

Understanding a statement about equivalent norms ($||\cdot ||_2 \sim||\cdot||_1 $)

Definition of CAT(0) metric space

Interior of a Dirichlet domain in a Riemannian manifold

metric-spaces closure

We know that a Compact set is closed. However a finite discreet set is compact but not closed (contradicting the theorem?)

prove that there is maximum and minimum for C[0,1]

Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?

Show that for any subsets $A,B\subset X$: (i):$d(A\bigcup B)\leq d(A)+d(B)+d(A,B)$ and (ii) $d(\bar A)=d(A)$

Does a (local) uniqueness theorem exist for geodesics in metric spaces?

Definition of disc and open ball

Lipschitz continuous set-valued map

Defining the integral on an arbitrary metric space

d' is finer than d on compact space $\implies$ $\forall \epsilon \ \ \exists \epsilon' \ \ \forall x \ B_{d'}(x,\epsilon') \subseteq B_d(x,\epsilon)$

Finsler Metric from page 2 of the book by Chern and Shen.

Isometry fixing an open set pointwise is identity

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