View source for Urysohn space

''space satisfying the Urysohn separation axiom''

A [[Topological space|topological space]] in which any two distinct points have neighbourhoods with disjoint closure.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  P.S. Aleksandrov,   P. Urysohn,   "Mémoire sur les espaces topologiques compacts" , Koninkl. Nederl. Akad. Wetensch. , Amsterdam  (1929)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  A.V. Arkhangel'skii,   V.I. Ponomarev,   "Fundamentals of general topology: problems and exercises" , Reidel  (1984)  pp. 125  (Translated from Russian)</TD></TR></table>



====Comments====
Regular <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095900/u0959001.png" />-spaces (cf. [[Regular space|Regular space]]; [[Separation axiom|Separation axiom]]) are Urysohn, and Urysohn spaces are Hausdorff (cf. [[Hausdorff space|Hausdorff space]]). Neither implication is reversible.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  R. Engelking,   "General topology" , Heldermann  (1989)</TD></TR></table>