7 papers
H-covering Maps in Descriptive Function Theory
Alexey Ostrovsky
We study the preservation of complete metrizability under maps between metric spaces. Two main approaches have been developed in this area: one based on the behavior of maps on cou…
Finite Decompositions for Initial Baire-1 Subclasses and Their Characterization via Homogeneous Sequences
Alexey Ostrovsky
We announce some results concerning initial subclasses of the Baire-1 functions. First, we obtain a finite decomposition into continuous maps for a basic initial subclass. Second,…
Open--constructible functions
Alexey Ostrovsky
We prove that if a continuous function takes open sets into elements of the Boolean algebra generated by open and closed subsets in , then there exist $X_n \…
Closed-Constructible functions are Piece-Wise Closed
Alexey Ostrovsky
A subset is constructible if it is an element of the smallest family that contains all open sets and is stable under finite intersections and complements. A function…
Preservation of the Borel class under open- functions
Alexey Ostrovsky
Let be a Borel subset of the Cantor set \textbf{C} of additive or multiplicative class and be a continuous function with compact preimages of points onto $Y \…
-homogeneity of Borel sets
Alexey Ostrovsky
We give an affirmative answer to the following question: Is any Borel subset of a Cantor set a sum of a countable number of pairwise disjoint -homogeneous subspace…
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…