arXiv subjects

Alexey Ostrovsky

Publications and source records attributed to Alexey Ostrovsky.

7 recordsLinked to original sources

arXiv2026

H-covering Maps in Descriptive Function Theory

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 countable compact sets, and another based on abstract conditions such as stability. In earlier work the author introduced the class of H-covering maps and proved that every such map is stable. The main result of this paper is the converse: a map is H-covering if and only if it is stable. This provides a concrete and practical description of stable maps and offers a unified framework for completeness-preserving mappings.

math.GN↗

arXiv2026

Finite Decompositions for Initial Baire-1 Subclasses and Their Characterization via Homogeneous Sequences

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, we give a pointwise description of initial subclasses via point-homogeneous sequences. Third, we present a finite decomposition of maps into open and closed maps.

math.GN↗

arXiv2014

Open--constructible functions

We prove that if a continuous function $f : X \to f(X)$ takes open sets into elements of the Boolean algebra generated by open and closed subsets in $f(X)$, then there exist $X_n \subset X,$ $(n \in ω)$ such that $f$ is open on every $X_n$ and $f(X_n)$ cover $ f(X).$

math.GN↗

arXiv2012

Closed-Constructible functions are Piece-Wise Closed

A subset $B \subset Y$ 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 $f : X \to Y$ is said to be piece-wise closed if $X$ can be written as a countable union of closed sets $Z_n$ such that $f$ is closed on every $Z_n.$ We prove that if a continuous function $f$ takes each closed set into a constructible subset of $Y$, then $f$ is piece-wise closed.

math.GN↗

arXiv2011

Countable open and closed functions

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 $X_i \subset X$ $ (i=1,2,...$) such that $f|X_i$ are open or closed functions onto $f(X_i)$ and $f(X_i)$ cover $Y.$

math.GN↗

arXiv2011

$σ$-homogeneity of Borel sets

We give an affirmative answer to the following question: Is any Borel subset of a Cantor set $\textbf{ C}$ a sum of a countable number of pairwise disjoint $h$-homogeneous subspaces that are closed in $X$? It follows that every Borel set $X \subset \textbf{ R}^n$ can be partitioned into countably many $h$-homogeneous subspaces that are $G_δ$-sets in $X$.

math.LO↗

arXiv2011

Preservation of the Borel class under open-$LC$ functions

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 $Y \subset \textbf{C}.$ 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. This result generalizes similar results for open and closed functions.

math.GN↗