On measurability of quasi-continuous and some related maps
type: Item
instance of: scholarly article
title: On measurability of quasi-continuous and some related maps
zbMATH Open document ID: 0649.54005
DOI: 10.1007/BF01848993
author: S. H. Smith
published in: Periodica Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 28A20
zbMATH DE Number: 4060275
MaRDI profile type: Publication
cites work: Q3260984
cites work: Semi-topological properties
cites work: Q3312895
cites work: Semi-Open Sets and Semi-Continuity in Topological Spaces
cites work: \(\alpha\)-continuous and \(\alpha\)-open mappings
cites work: On some classes of nearly open sets
full work available at URL: https://doi.org/10.1007/bf01848993
OpenAlex ID: W2086239474
description: scientific article; zbMATH DE number 4060275