# Urysohn space

From Encyclopedia of Mathematics

*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) |

**How to Cite This Entry:**

Urysohn space.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Urysohn_space&oldid=32855

This article was adapted from an original article by B.A. Efimov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article