Namespaces
Variants
Actions

Urysohn space

From Encyclopedia of Mathematics
Revision as of 17:24, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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 -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://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