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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Completions of uniform convergence spaces


Author: G. D. Richardson
Journal: Proc. Amer. Math. Soc. 29 (1971), 159-164
MSC: Primary 54.30
DOI: https://doi.org/10.1090/S0002-9939-1971-0282332-5
MathSciNet review: 0282332
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Abstract: H. J. Biesterfeldt has shown that a uniform convergence space which satisfies the completion axiom has a completion. In the present paper, we show that every uniform convergence space has a completion. Furthermore, if the uniform convergence space is Hausdorff and satisfies the completion axiom, then it has a Hausdorff completion, which reduces to the Bourbaki completion for uniform spaces. Finally, a uniqueness theorem is obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0282332-5
Keywords: Uniform convergence space, completion, Cauchy filter, uniform isomorphism
Article copyright: © Copyright 1971 American Mathematical Society

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