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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.


References [Enhancements On Off] (What's this?)

  • [1] M. S. Gagrat and S. A. Naimpally, Proximity approach to extension problems, Fund. Math. 71 (1971), 63-76. MR 45 #2653. MR 0293576 (45:2653)
  • [2] H. Herrlich, Topological functors, General Topology and Appl. (to appear). MR 0343226 (49:7970)
  • [3] H. Herrlich and G. Strecker, Category theory, Allyn and Bacon, Boston, Mass., 1973. MR 0349791 (50:2284)
  • [4] P. L. Sharma and S. A. Naimpally, Construction of Lodato proximities, Math. Japon. 15 (1970), 101-103. MR 44 #4709. MR 0287505 (44:4709)
  • [5] P. L. Sharma, Proximity bases and subbases, Pacific J. Math. 37 (1971), 515-526. MR 46 #4488. MR 0305358 (46:4488)

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Additional Information

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

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