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Finite-to-one continuous s-covering mappings

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Ostrovsky A.

Fundamenta Mathematicae

2007

tom 194

nr 1

89-93

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.

Preservation of the Borel class under open-LC functions

100%

Ostrovsky A.

Fundamenta Mathematicae

2011

tom 213

nr 2

191-195

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.

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2 Fundamenta Mathematicae

2 Ostrovsky A.

1 2011

1 2007

Wyniki wyszukiwania

Finite-to-one continuous s-covering mappings

Preservation of the Borel class under open-LC functions