Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on uniform paracompactness


Author: Michael D. Rice
Journal: Proc. Amer. Math. Soc. 62 (1977), 359-362
MSC: Primary 54E15; Secondary 54D20
MathSciNet review: 0436085
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Three possible definitions for the paracompactness of a uniform space are presented and shown to be equivalent. A locally compact uniform space is shown to be uniformly paracompact if and only if it is uniformly locally compact. The set of points of a uniformly paracompact metric space that admit no compact neighborhood is shown to be compact; hence a metric topological group is uniformly paracompact if and only if it is locally compact.


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

  • [I] J. R. Isbell, Uniform spaces, Math Surveys, no. 12, Amer. Math. Soc., Providence, R. I., 1964. MR 30 #561. MR 0170323 (30:561)
  • [R] M. D. Rice, Complete uniform spaces, TOPO 72-General Topology and Its Applications (Proc. 2nd Pittsburgh Internat. Conf., Carnegie-Mellon Univ. and Univ. of Pittsburgh, Pittsburgh, Pa., 1972), Lecture Notes in Math., vol. 378, Springer, Berlin, 1974. MR 50 #11166. MR 0358707 (50:11166)
  • [So] R. H. Sorgenfrey, On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947), 631-632. MR 8, 594. MR 0020770 (8:594f)
  • [St] A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977-982. MR 10, 204. MR 0026802 (10:204c)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54E15, 54D20

Retrieve articles in all journals with MSC: 54E15, 54D20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0436085-3
PII: S 0002-9939(1977)0436085-3
Keywords: Uniformly locally finite open cover, paracompact, uniformly paracompact, locally compact, uniformly locally compact
Article copyright: © Copyright 1977 American Mathematical Society