Proximity space

In topology, a proximity space, also called a nearness space, is an axiomatization of notions of "nearness" that hold set-to-set, as opposed to the better known point-to-set notions that characterize topological spaces.

The concept was described by FrigyesRiesz (1909) but ignored at the time. It was rediscovered and axiomatized by V. A. Efremovič in 1934 under the name of infinitesimal space, but not published until 1951. In the interim, A. D.Wallace (1941) discovered a version of the same concept under the name of separation space.