# 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 $x\in A$ and $$\sup_{a\in A} d(x,a) = \inf_{b\in A} \sup_{a\in A} d(b,a)$$.

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