Urysohn space

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space satisfying the Urysohn separation axiom

A topological space in which any two distinct points have neighbourhoods with disjoint closure.


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


Regular $T_1$-spaces (cf. Regular space; Separation axiom) are Urysohn, and Urysohn spaces are Hausdorff (cf. Hausdorff space). Neither implication is reversible.


[a1] R. Engelking, "General topology" , Heldermann (1989)
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Urysohn space. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by B.A. Efimov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article