A. Ostrovsky

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20112026

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math.GN2011

Preservation of the Borel class under open- $L C$ functions

Alexey Ostrovsky

Let $X$ be a Borel subset of the Cantor set \textbf{C} of additive or multiplicative class $α,$ and $f : X \to Y$ be a continuous function with compact preimages of points onto $Y \…

math.LO2011

$σ$ -homogeneity of Borel sets

Alexey Ostrovsky

We give an affirmative answer to the following question: Is any Borel subset of a Cantor set $C$ a sum of a countable number of pairwise disjoint $h$ -homogeneous subspace…

math.GN2011

Countable open and closed functions

Alexey Ostrovsky

We define two natural classes of functions, called 2-open and 2-closed, that are closest to open and closed functions. We show that they have the following property: there are $X_i…

Preservation of the Borel class under open-LC functions

σ-homogeneity of Borel sets

Countable open and closed functions

Preservation of the Borel class under open- $L C$ functions

$σ$ -homogeneity of Borel sets