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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

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