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Open finite-to-one mappings on p-spaces. (English) Zbl 0531.54025
A (completely regular) topological space X is a p-space if in $$\beta$$ X (the Stone-Čech compactification of X) there is a family $$\Phi$$ of coverings of X by open subsets of $$\beta$$ X such that $$\cap \{\lambda(x):\quad \lambda \in \Phi \}\subset X$$ for each $$x\in X$$ (where $$\lambda(x)=\cup \{U:\quad x\in U\quad and\quad U\in \lambda \}).$$ This notion was introduced by A. J. Arkhangelskij who showed that a space is a paracompact p-space if and only if it is the preimage of a metric space under a perfect map. It is shown that if f is a finite-to-one, continuous, open mapping from a (completely regular) p-space X onto a (completely regular) space Y, then Y is also a p-space.
Reviewer: S.Broverman

MSC:
 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54E18 $$p$$-spaces, $$M$$-spaces, $$\sigma$$-spaces, etc.