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Products of Steiner's quasi-proximity spaces

Author: E. Hayashi
Journal: Proc. Amer. Math. Soc. 51 (1975), 225-230
MSC: Primary 54E05
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, $ \delta $-continuous maps
Article copyright: © Copyright 1975 American Mathematical Society

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