# 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)

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