Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A short proof that metric spaces are realcompact


Author: M. D. Rice
Journal: Proc. Amer. Math. Soc. 32 (1972), 313-314
MSC: Primary 54.35
DOI: https://doi.org/10.1090/S0002-9939-1972-0288724-3
MathSciNet review: 0288724
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A short proof is given that metric spaces which have no closed discrete subspaces of measurable cardinal are realcompact. This result is used to obtain the Shirota theorem that topologically complete spaces which have no closed discrete subspaces of measurable cardinal are realcompact.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.35

Retrieve articles in all journals with MSC: 54.35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288724-3
Keywords: Realcompact, topologically complete, ultrafilter, measurable cardinal
Article copyright: © Copyright 1972 American Mathematical Society