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Proceedings of the American Mathematical Society

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

 

 

Tychonoff reflection in products and the $ \omega$-topology on function spaces


Author: Stephen Watson
Journal: Proc. Amer. Math. Soc. 108 (1990), 557-559
MSC: Primary 54C35; Secondary 54B10, 54D45
DOI: https://doi.org/10.1090/S0002-9939-1990-1007518-5
MathSciNet review: 1007518
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Abstract: We show that if $ X$ is a topological space such that $ CR(X)$, the topology on $ X$ generated by the cozero sets, is not locally compact, then there is a regular space $ Y$ such that $ CR(X \times Y) \ne CR(X) \times CR(Y)$. We use the $ \omega $-topology on the space of continuous functions $ C\left( {X,Y} \right)$ (where $ \omega $ is an open cover of $ X$) which was defined by Arens and Dugundji in 1950.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1007518-5
Article copyright: © Copyright 1990 American Mathematical Society