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Preservation of the Borel class under open-LC functions

Alexey Ostrovsky — 2011

Fundamenta Mathematicae

Let X be a Borel subset of the Cantor set C of additive or multiplicative class α, and f: X → Y be a continuous function onto Y ⊂ C with compact preimages of points. If the image f(U) of every clopen set U is the intersection of an open and a closed set, then Y is a Borel set of the same class α. This result generalizes similar results for open and closed functions.

Finite-to-one continuous s-covering mappings

Alexey Ostrovsky — 2007

Fundamenta Mathematicae

The following theorem is proved. Let f: X → Y be a finite-to-one map such that the restriction f | f - 1 ( S ) is an inductively perfect map for every countable compact set S ⊂ Y. Then Y is a countable union of closed subsets Y i such that every restriction f | f - 1 ( Y i ) is an inductively perfect map.

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