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Proceedings of the American Mathematical Society

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

 
 

 

Products of Steiner’s quasi-proximity spaces


Author: E. Hayashi
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
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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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Keywords: Quasi-proximity, product proximity, <IMG WIDTH="15" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\delta$">-continuous maps
Article copyright: © Copyright 1975 American Mathematical Society