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Uniformities with totally ordered bases have paracompact topologies

Published online by Cambridge University Press:  24 October 2008

Allan Hayes
Allan Hayes
Affiliation:
University of Leicester
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Extract

This result does not appear to be in the literature, though the method of proof is related to those used in (1) and, particularly, (2) to prove A. H. Stone's theorem that metrics have paracompact topologies.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 67 - 68
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Ornstein, D.A new proof of the paracompactness of metric spaces. Proc. Amer. Math. Soc. 21 (1969), 341–342.CrossRefGoogle Scholar
(2)Rudin, M. F.A new proof that metric spaces are paracompact. Proc. Amer. Math. Soc. 20 (1969), 603.CrossRefGoogle Scholar
(3)Kelley, J. L.General topology (New York, 1955).Google Scholar