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Remainders of metric completions
Published online by Cambridge University Press: 17 April 2009
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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