Editing Proximity space (section)

{{short description|Structure describing a notion of "nearness" between subsets}}
In [[topology]], a '''proximity space''', also called a '''nearness space''', is an axiomatization of the intuitive notion of "nearness" that hold set-to-set, as opposed to the better known point-to-set notion that characterize [[topological space]]s.

The concept was described by {{harvs|txt|authorlink=Frigyes Riesz|first=Frigyes |last=Riesz|year= 1909}} but ignored at the time.<ref>W. J. Thron, ''Frederic Riesz' contributions to the foundations of general topology'', in C.E. Aull and R. Lowen (eds.), ''Handbook of the History of General Topology'', Volume 1, 21-29, Kluwer 1997.</ref> It was rediscovered and axiomatized by [[Vadim Arsenyevich Efremovich|V. A. Efremovič]] in 1934 under the name of '''infinitesimal space''', but not published until 1951. In the interim, {{harvs|txt|first=A. D. |last=Wallace|authorlink=A. D. Wallace|year=1941}} discovered a version of the same concept under the name of '''separation space'''.