On measurability of quasi-continuous and some related maps
Let X, Y be topological spaces, \({\mathcal A}\) any family of maps from X into Y. \({\mathcal S}({\mathcal A})\) denotes the smallest \(\sigma\)-algebra of subsets of X with respect to which all maps belonging to \({\mathcal A}\) are measurable. If X is a perfectly normal space, Y is a \(T_ 1\)-space with at least two points and \({\mathcal A}\) consists of all quasi-continuous maps [\textit{S. Kempisty}, Fundam. Math. 19, 184-197 (1932; Zbl 0005.19802)] (resp. irresolute maps [\textit{S. G. Crossley} and \textit{S. K. Hildebrand}, Fundam. Math. 74, 233-254 (1972; Zbl 0206.515)]) then \({\mathcal S}({\mathcal A})\) coincides with the \(\sigma\)-algebra of sets with the Baire property. For upper and lower measurability of multivalued maps analogous theorems are true.
scientific article; zbMATH DE number 4060275