Namespaces
Variants
Actions

Difference between revisions of "Urysohn metrization theorem"

From Encyclopedia of Mathematics
Jump to: navigation, search
m (Added category TEXdone)
(Category:General topology)
Line 10: Line 10:
 
<TR><TD valign="top">[a3]</TD> <TD valign="top"> W.Franz,  "General topology" , Harrap  (1967)  p. 100</TD></TR>
 
<TR><TD valign="top">[a3]</TD> <TD valign="top"> W.Franz,  "General topology" , Harrap  (1967)  p. 100</TD></TR>
 
</table>
 
</table>
 +
 +
[[Category:General topology]]

Revision as of 19:57, 15 October 2014

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 (cf. Normal space), or (an addition by A.N. Tikhonov) if and only if it is regular.

References

[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: http://encyclopediaofmath.org/index.php?title=Urysohn_metrization_theorem&oldid=33671
This article was adapted from an original article by P.S. Aleksandrov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article