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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Products of $ k$-spaces and spaces of countable tightness


Authors: G. Gruenhage and Y. Tanaka
Journal: Trans. Amer. Math. Soc. 273 (1982), 299-308
MSC: Primary 54D50; Secondary 54C10, 54D55
DOI: https://doi.org/10.1090/S0002-9947-1982-0664043-9
MathSciNet review: 664043
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Abstract: In this paper, we obtain results of the following type: if $ f:X \to Y$ is a closed map and $ X$ is some "nice" space, and $ {Y^2}$ is a $ k$-space or has countable tightness, then the boundary of the inverse image of each point of $ Y$ is "small" in some sense, e.g., Lindelöf or $ {\omega _1}$-compact. We then apply these results to more special cases. Most of these applications combine the "smallness" of the boundaries of the point-inverses obtained from the earlier results with "nice" properties of the domain to yield "nice" properties on the range.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0664043-9
Article copyright: © Copyright 1982 American Mathematical Society