A note on uniform paracompactness
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- by Michael D. Rice PDF
- Proc. Amer. Math. Soc. 62 (1977), 359-362 Request permission
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
- J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170323
- Michael D. Rice, Complete uniform spaces, TOPO 72—general topology and its applications (Proc. Second Pittsburgh Internat. Conf., Pittsburgh, Pa., 1972; dedicated to the memory of Johannes H. de Groot), Lecture Notes in Math., Vol. 378, Springer, Berlin, 1974, pp. 399–418. MR 0358707
- R. H. Sorgenfrey, On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947), 631–632. MR 20770, DOI 10.1090/S0002-9904-1947-08858-3
- A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977–982. MR 26802, DOI 10.1090/S0002-9904-1948-09118-2
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 359-362
- MSC: Primary 54E15; Secondary 54D20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0436085-3
- MathSciNet review: 0436085