Ideal equivalences for almost real-compact spaces
Inserting measurable functions precisely
A family of subsets of a set is called a -topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A -topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect -topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a -topological version of Katětov-Tong...
Insertion of a Contra-Baire- (Baire-) Function
Necessary and sufficient conditions in terms of lower cut sets are given for the insertion of a Baire- function between two comparable real-valued functions on the topological spaces that -kernel of sets are -sets.