On σ-porous sets and Borel sets

On Σ-porous Sets in Abstract Spaces

The main aim of this survey paper is to give basic information about properties and applications of σ-porous sets in Banach spaces (and some other infinite-dimensional spaces). This paper can be considered a partial continuation of the author’s 1987 survey on porosity and σ-porosity and therefore only some results, remarks, and references (important for infinite-dimensional spaces) are repeated...

On Borel Mappings and Σ-ideals Generated by Closed Sets

We obtain some results about Borel maps with meager fibers on completely metrizable separable spaces. The results are related to a recent dichotomy by Sabok and Zapletal, concerning Borel maps and σ-ideals generated by closed sets. In particular, we give a “classical” proof of this dichotomy. We shall also show that for certain natural σ-ideals I generated by closed sets in compact metrizable s...

Inscribing Closed Non-σ-lower Porous Sets into Suslin Non-σ-lower Porous Sets

This paper is a continuation of the work done in [9]. We are interested in the following question within the context of σ-ideals of σ-porous type. Let X be a metric space and let be a σ-ideal of subsets of X . Let S⊂ X be a Suslin set with S / ∈ . Does there exist a closed set F ⊂ S which is not in ? The answer is positive provided that X is locally compact and is a σ-ideal of σP-porous sets, w...

A Course on Borel Sets

On Borel Sets Belonging to Every Invariant Ccc Σ-ideal on 2n

Let Iccc be the σ-ideal of subsets of the Cantor group 2N generated by Borel sets which belong to every translation invariant σ-ideal on 2N satisfying the countable chain condition (ccc). We prove that Iccc strongly violates ccc. This generalizes a theorem of Balcerzak-Rosłanowski-Shelah stating the same for the σ-ideal on 2N generated by Borel sets B ⊆ 2N which have perfectly many pairwise dis...