Urysohn metrization theorem

From Encyclopedia of Mathematics
Revision as of 19:59, 15 October 2014 by Richard Pinch (talk | contribs) (better)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

A compact or countably compact Hausdorff space is metrizable if and only if it has a countable base: indeed, it is homeomorphic to a subset of the Hilbert cube.

A topological space with a countable base is metrizable if and only if it is normal, or (an addition by A.N. Tikhonov) if and only if it is regular.


[a1] A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) pp. Chapt. 5 (Translated from Russian)
[a2] J.L. Kelley, "General topology" , v. Nostrand (1955) pp. 125; 127
[a3] W.Franz, "General topology" , Harrap (1967) p. 100
How to Cite This Entry:
Urysohn metrization theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by P.S. Aleksandrov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article