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Results tagged with metric-spaces
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user 122026
A metric space is a pair $(X,d)$, where $X$ is a set and $d:X \times X \to \mathbb{R}$ satisfies the following conditions for all $x,y,z \in X$. (Symmetry) $d(x,y)=d(y,x)$. (Identity of Indiscernibles) $d(x,y)=0$ if and only if $x=y$. (Triangle Inequality) $d(x,y)+d(y,z) \geq d(x,z)$.
25
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Accepted
A funny metric over $\mathbb{N}$
This metric is mentioned in the Encyclopedia of distances (Chapter 10.3), written by Michel Marie Deza and Elena Deza. Here is the relevant paragraph:$\newcommand{\lcm}{\operatorname{lcm}}$
Let $\mat …
- 8,401
2
votes
Accepted
Divergence functions in hyperbolic groups
There exist many non-hyperbolic groups with superlinear divergence. For instance:
One-ended relatively hyperbolic groups have exponential divergence. (See Sisto's article On metric relative hyperboli …
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