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Suppose I am given a finite metric space as a distance matrix. What is the complexity of determining whether this metric space is hyperconvex? Definition: A metric space is said to be hyperconvex if ...

A direct line from a point $p$ to a set $X$ is a line segment with one endpoint at $p$ and one endpoint in $X$, which is as short as any other line segment from $p$ to $X$. Given a closed set $X$ and ...

I am looking for a proof of the following statement: Let $X$ be a complete Busemann space. For any point $x\in X$ and any nonempty closed convex set $A\subseteq X$, there is a unique $a\in A$ such ...

Let $( \mathbb{R}^d, \| \mathbf{x}\|_2 )$ be a Euclidean Space. For any nonempty closed convex set $A\subseteq \mathbb{R}^d$, we define \begin{align} d(\mathbf{x}, A) = \inf \{ \| \mathbf{x} - \mathbf{...