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Remainders of metric completions

Published online by Cambridge University Press:  17 April 2009

C.J. Knight
C.J. Knight
Affiliation:
Department of Pure Mathematics, University of Sheffield, Sheffield, England.
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Abstract

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Certain topological spaces X may bear various uniform structures compatible with the topology of X; to each uniform structure there corresponds a completion of X, that is, a complete space Z containing X as a dense subspace. For compact completions, there has been extensive study of the relationship between X and the possible remainders Z\X. This paper begins a study of the more general, and apparently easier, problem of the relationship between X and its not necessarily compact remainders. We find that for spaces X admitting a complete metric, every space Y which satisfies certain conditions obviously necessary for Y to be the remainder of a completion of X in fact occurs as such a completion.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 3 , December 1972 , pp. 367 - 376
Copyright
Copyright © Australian Mathematical Society 1972

References

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