Tychonoff reflection in products and the $\omega$-topology on function spaces
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- by Stephen Watson PDF
- Proc. Amer. Math. Soc. 108 (1990), 557-559 Request permission
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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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