Infinite combinatorics in Function spaces: Category methods
Inscribing closed non--lower porous sets into Suslin non--lower porous sets.
Inscribing compact non-σ-porous sets into analytic non-σ-porous sets
The main aim of this paper is to give a simpler proof of the following assertion. Let A be an analytic non-σ-porous subset of a locally compact metric space, E. Then there exists a compact non-σ-porous subset of A. Moreover, we prove the above assertion also for σ-P-porous sets, where P is a porosity-like relation on E satisfying some additional conditions. Our result covers σ-⟨g⟩-porous sets, σ-porous sets, and σ-symmetrically porous sets.
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...
Invariance of Borel Classes in Metric Spaces.
Iterated products of ideals of Borel sets