Urysohn space
From Encyclopedia of Mathematics - Reading time: 1 min
space satisfying the Urysohn separation axiom
A topological space in which any two distinct points have neighbourhoods with disjoint closure.
Comments[edit]
Regular $T_1$-spaces (cf. Regular space; Separation axiom) are Urysohn, and Urysohn spaces are Hausdorff (cf. Hausdorff space). Neither implication is reversible.
References[edit]
| [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) |
| [a1] | R. Engelking, "General topology" , Heldermann (1989) |
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