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Proceedings of the American Mathematical Society

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

 

 

Extensions of proximity functions


Author: Don A. Mattson
Journal: Proc. Amer. Math. Soc. 26 (1970), 347-351
MSC: Primary 54.30
DOI: https://doi.org/10.1090/S0002-9939-1970-0264631-5
MathSciNet review: 0264631
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Abstract: Let $ {P^ \ast }(X)$ be the algebra of bounded, real-valued proximity functions on a proximity space $ (X,\delta )$, where $ X$ is a dense subspace of a topological space $ T$. In this paper we obtain several conditions which are equivalent to the following property: every member of $ {P^ \ast }(X)$ has a continuous extension to $ T$. Examples concerning these results are included, one of which shows that this extension property is distinct from $ {C^ \ast }$-embedding.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0264631-5
Keywords: Proximity space, $ p$-subspaces, algebras of bounded realvalued proximity functions, Smirnov compactification, $ {C^ \ast }$-embedding, round filters, gauges, continuous extension of functions, Stone-Čech compactification
Article copyright: © Copyright 1970 American Mathematical Society