Urysohn space
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
space satisfying the Urysohn separation axiom
A topological space in which any two distinct points have neighbourhoods with disjoint closure.
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
| [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) |
How to Cite This Entry:
Urysohn space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Urysohn_space&oldid=53676
Urysohn space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Urysohn_space&oldid=53676
This article was adapted from an original article by B.A. Efimov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article