Is this a metric: $d\big((\mathbf{x},A_x),(\mathbf{y},A_y)\big)=\frac{1}{2}(\mathbf{x}-\mathbf{y})^\top\big(A_x+A_y\big)^{-1}(\mathbf{x}-\mathbf{y})$?

score 141 · Answer 7 · 2026-04-14 09:31:33

141

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Using uniform continuity to decompose a path in the complex plane

Published on 14 Apr 2026 - 9:31

score 133 · Answer 8 · 2026-04-12 04:30:57

133

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Use contraction mapping theorem to prove

Published on 12 Apr 2026 - 4:30

score 41 · Answer 9 · 2026-04-12 15:30:28

41

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Some neigbourhood properties

Published on 12 Apr 2026 - 15:30

score 12.1k · Answer 10 · 2026-04-14 11:13:51

12.1k

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closure = union of the set and the set of limit points

Published on 14 Apr 2026 - 11:13

score 58 · Answer 11 · 2026-04-11 20:17:58

58

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Problem showing that $\partial D = \emptyset$

Published on 11 Apr 2026 - 20:17

score 262 · Answer 12 · 2026-04-15 19:18:38

Let $(X,d)$ be a metric space and $M\subset X$ is uncountable. There is $\alpha>0$ such that $d(x,y)=\alpha$. Prove that $X$ is not separable.

score 1.7k · Answer 13 · 2026-04-16 02:07:56

1.7k

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Mary Ellen Rudin's proof that all metric space are paracompact

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score 1.5k · Answer 14 · 2026-04-13 17:12:05

1.5k

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Every $K$-Lipschitz function can be uniformly approximated by $C^1$ functions with derivative bounded by $K$

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score 203 · Answer 15 · 2026-04-09 23:55:21

203

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The metric identification of a pseudometric on $C(\mathbb{I})$

Published on 09 Apr 2026 - 23:55

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Is this a metric: $d\big((\mathbf{x},A_x),(\mathbf{y},A_y)\big)=\frac{1}{2}(\mathbf{x}-\mathbf{y})^\top\big(A_x+A_y\big)^{-1}(\mathbf{x}-\mathbf{y})$?

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