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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Products of Steiner’s quasi-proximity spaces
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by E. Hayashi PDF
Proc. Amer. Math. Soc. 51 (1975), 225-230 Request permission

Abstract:

E. F. Steiner introduced a quasi-proximity $\delta$ satisfying $A\delta B \operatorname {iff}\; \{ x\} \delta B$ for some $x$ of $A$. The purpose of this paper is to describe the Tychonoff product of topologies in terms of Steiner’s quasi-proximities. Whenever $({X_a},{\delta _a})$ is the Steiner quasi-proximity space, the product proximity on $X = \Pi {X_a}$ can be given, by using the concept of finite coverings, as the smallest proximity on $X$ which makes each projection $\delta$-continuous.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 225-230
  • MSC: Primary 54E05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0370512-3
  • MathSciNet review: 0370512