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Proceedings of the American Mathematical Society

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

 

 

Proximity spaces and topological functors


Authors: W. N. Hunsaker and P. L. Sharma
Journal: Proc. Amer. Math. Soc. 45 (1974), 419-425
MSC: Primary 54E05
DOI: https://doi.org/10.1090/S0002-9939-1974-0353265-3
MathSciNet review: 0353265
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Abstract: The purpose of this paper is to determine what natural functors $ T:{\mathbf{A}} \to {\mathbf{X}}$ are $ (\mathcal{E},\mathfrak{M})$-topological, where $ {\mathbf{A}}$ is a subcategory of the category of proximity or uniform spaces and $ {\mathbf{X}}$ is an $ (\mathcal{E},\mathfrak{M})$-category. We give necessary and sufficient conditions under which a point separating family of continuous functions can be nicely lifted to a proximally continuous family. Proximities having a finest compatible uniform structure are characterized.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0353265-3
Keywords: Source, absolutely topological functor, LO-proximity, EF-proximity, uniformity, proximity class, weak proximity
Article copyright: © Copyright 1974 American Mathematical Society