Urysohn space

space satisfying the Urysohn separation axiom

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

References

[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)

Comments

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

References

[a1]	R. Engelking, "General topology" , Heldermann (1989)