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Inscribing compact non-σ-porous sets into analytic non-σ-porous sets

Miroslav Zelený, Luděk Zajíček (2005)

Fundamenta Mathematicae

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

Javier Gutiérrez García, Tomasz Kubiak (2014)

Czechoslovak Mathematical Journal

A family of subsets of a set is called a σ -topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A σ -topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect σ -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 σ -topological version of Katětov-Tong...

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