Borsuk-Ulam type theorems for metric spaces
  In this paper we study the problems of the following kind: For a pair of topological spaces $X$ and $Y$ find sufficient conditions that under every continuous map $f : X\to Y$ a pair of sufficiently distant points is mapped to a single point. 
Arseniy Akopyan, Roman Karasev, and Alexey Volovikov
math.MG math.AT