Finite-to-one continuous $s$-covering mappings
Volume 194 / 2007
Fundamenta Mathematicae 194 (2007), 89-93
MSC: Primary 54C10, 54H05, 54E40.
DOI: 10.4064/fm194-1-5
Abstract
The following theorem is proved. Let $f: X \to Y$ be a finite-to-one map such that the restriction $f|f^{-1}(S)$ is an inductively perfect map for every countable compact set $S \subset Y$. Then $Y$ is a countable union of closed subsets $Y_i$ such that every restriction $f|f^{-1}(Y_i)$ is an inductively perfect map.
