Tagged Questions

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What's the real name for these things? Categories whose morphisms have “length.”

A fairly obvious "categorification" of metric spaces is as follows. First, let us agree to view $\mathbb{R}_+$ as an ordered Abelian monoid, where by "Abelian monoid" we really mean a category whose ...
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proper term for a center of a set in a metric space

I want to know if there is a proper term for the following kind of points, which I call it center(borrowed from graph theory). Let $(X,d)$ be a metric space. $x\in X$ is a center of $A\subset X$ if ...
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What is the correct distance measure for the (anti) de-Sitter space?

Given these two expressions 1) $\sinh{d}=\frac{\sqrt{t^2−x^2}}{\sqrt{1−(t^2−x^2)}}$ 2) $\sin{d}=\frac{\sqrt{t^2−x^2}}{\sqrt{1+(t^2−x^2)}}$ for distance $d$ from the origin $(0,0)$ to point $(x,t)$, ...
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What is the proper term for the entity that relates a vector space and a set?

One way to generate a metric for a set $S$ (a distance function between elements $a,b$ of the set $S$) would be by associating it with a vector space $V$ (the vectors that connect the elements $a,b$) ...
Let $X$ be a set, and $d,d'$ two metrics on $X$. Consider the identity map $i : (X,d) \to (X,d')$ as a map of metric spaces. There are (at least) three reasonable notions of equivalence for $d$ and ...