A. Osipov

activity

20112023

most citedGroup structures of a function spaces with the set-open topology

5 citations · 15 across the 39 of their papers we have counts for

collaborators

52 papers

math.MG2023

A two dimensional analog of the three gap theorem

Yury Kochetkov, Alexandr Osipov

For a two dimensional vector $v ˉ = (α, β)$ , where $α > 0, β > 0$ are irrational numbers independent over $Q$ , we consider the set $D_n=\{(iα\,{\rm mod}\,1,iβ\,{\rm mod}\,1),i…

math.GN2023

Generalization of the Grothendieck's theorem

Mikhail Al'perin, Alexander V. Osipov

In this paper, we have obtained a generalization of the Grothendieck's theorem for the space of continuous mappings $C_{λ, μ} (X, Y)$ where $Y$ is a complete uniform space with the un…

math.GN2023

Some observations on a clopen version of the Rothberger property

Manoj Bhardwaj, Alexander V. Osipov

In this paper, we proved that a clopen version $S_{1} (C_{O}, C_{O})$ of the Rothberger property and Borel strong measure zeroness are independent. For a zero-dimensional metric space $(X…

math.GN2023

Covering games using semi-open sets

Manoj Bhardwaj, Alexander V. Osipov

In this paper, we prove the following Theorems 1. An extremally disconnected space $X$ has the semi-Menger property if and only if One does not have a winning strategy in the game…

math.GN2023

The projectively Hurewicz property is t-invariant

Alexander V. Osipov

A space $X$ is projectively Hurewicz provided every separable metrizable continuous image of $X$ is Hurewicz. In this paper we prove that the projectively Hurewicz property is $t$ -…

math.GN2023

Frechet-Urysohn property of quasicontinuous functions

Alexander V. Osipov

The aim of this paper is to study the Frechet-Urysohn property of the space $Q_{p} (X, R)$ of real-valued quasicontinuous functions, defined on a Hausdorff space $X$ , endowed…

math.GN2022

On Baire property, compactness and completeness properties of spaces of Baire functions

Alexander V. Osipov

A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is dense in $X$ . One of the interesting problems for the space of Baire functions…

math.GN2022

On the first Banach problem, concerning condensations of absolute $κ$ -Borel sets onto compacta

Alexander V. Osipov

It is consistent that the continuum be arbitrary large and no absolute $κ$ -Borel set $X$ of density $κ$ , $ℵ_{1} < κ < c$ , condenses onto a compact metric space. It is con…

math.GN2022

Baireness of the space of pointwise stabilizing functions of the first Baire class

Alexander V. Osipov

A topological space $X$ is Baire if the Baire Category Theorem holds for $X$ , i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$ . In this paper, we…

math.GN2022

Spaces of Real Functions, Covers and Dense Subsets

Lev Bukovský, Alexander V. Osipov

In paper we study relationships between covering properties of a topological space $X$ and the space $(U S C^{*} (X), τ_{B})$ of bounded upper semicontinuous functions on $X$ w…

math.GN2022

Baire property of spaces of $[0, 1]$ -valued continuous functions

Alexander V. Osipov, Evgenii G. Pytkeev

A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is dense in $X$ . Let $C_{p} (X, [0, 1])$ denote the space of all continuous $[0, 1]$ -val…

math.GN2022★ 1 cited

Mildly version of Hurewicz Basis covering property and Hurewicz measure zero spaces

Manoj Bhardwaj, Alexander V. Osipov

In this paper, we introduced the mildly version of the Hurewicz basis covering property, studied by Babinkostova, Kočinac, and Scheepers. A space $X$ is said to have mildly-Hurewic…

math.GN2022

Every metric space of weight $λ = λ^{ℵ_{0}}$ admits a condensation onto a Banach space

Alexander V. Osipov, Evgenii G. Pytkeev

In this paper, we have proved that for each cardinal number $λ$ such that $λ = λ^{ℵ_{0}}$ a metric space of weight $λ$ admits a bijective continuous mapping onto a Banach space of…

math.GN2022★ 1 cited

Some observations on the mildly Menger property and topological games

Manoj Bhardwaj, Alexander V. Osipov

In this paper, we defined two new games - the mildly Menger game and the compact-clopen game. In a zero-dimensional space, the Menger game is equivalent to the mildly Menger game a…

math.GN2021★ 1 cited

Note on the Banach Problem 1 of condensations of Banach spaces onto compacta

Alexander V. Osipov

It is consistent with any possible value of the continuum $c$ that every infinite-dimensional Banach space of density $\leq c$ condenses onto the Hilbert cube…

math.GN2021

Embedding Theorems for function spaces

Mikhail Al'perin, Sergei Nokhrin, Alexander V. Osipov

In this paper, we have proved results similar to Tychonoff's Theorem on embedding a space of functions with the topology of pointwise convergence into the Tychonoff product of topo…

math.GN2021

Baire property of space of Baire-one functions

Alexander V. Osipov

A topological space $X$ is Baire if the Baire Category Theorem holds for $X$ , i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$ . One of the intere…

math.RA2021

Various types of completeness in topologized semilattices

Konstantin Kazachenko, Alexander V. Osipov

A topologized semilattice $X$ is called complete if each non-empty chain $C \subset X$ has $in f C$ and $sup C$ that belong to the closure $C$ of the chain $C$ in $X$ . In this pape…

math.GN2020

Topological properties of some function spaces

Saak Gabriyelyan, Alexander V. Osipov

Let $Y$ be a metrizable space containing at least two points, and let $X$ be a $Y_{I}$ -Tychonoff space for some ideal $I$ of compact sets of $X$ . Denote by $C_{…

math.GN2020★ 1 cited

On homeomorphism groups and the set-open topology

Alexander V. Osipov

In this paper we focus on the set-open topologies on the group $H (X)$ of all self-homeomorphisms of a topological space $X$ which yield continuity of both the group opera…

math.GN2020

On regular $κ$ -bounded spaces admitting only constant continuous mappings into $T_{1}$ spaces of pseudo-character $\leq κ$

Serhii Bardyla, Alexander V. Osipov

In this paper for each cardinal $κ$ we construct an infinite $κ$ -bounded (and hence countably compact) regular space $R_{κ}$ such that for any $T_{1}$ space $Y$ of pseudo-character $\l…

math.GN2019

On Ramsey properties, function spaces, and topological games

Steven Clontz, Alexander V. Osipov

An open question of Gruenhage asks if all strategically selectively separable spaces are Markov selectively separable, a game-theoretic statement known to hold for countable spaces…

math.GN2019

Selectors for dense subsets of function spaces

Lev Bukovský, Alexander V. Osipov

Let $U S C_{p}^{*} (X)$ be the topological space of real upper semicontinuous bounded functions defined on $X$ with the subspace topology of the product topology on $^{X} R$ . $\ti…

math.GN2019

Strongly sequentially separable function spaces, via selection principles

Alexander V. Osipov, Piotr Szewczak, Boaz Tsaban

A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and re…

A two dimensional analog of the three gap theorem

Generalization of the Grothendieck's theorem

Some observations on a clopen version of the Rothberger property

Covering games using semi-open sets

The projectively Hurewicz property is t-invariant

Frechet-Urysohn property of quasicontinuous functions

On Baire property, compactness and completeness properties of spaces of Baire functions

On the first Banach problem, concerning condensations of absolute κ-Borel sets onto compacta

Baireness of the space of pointwise stabilizing functions of the first Baire class

Spaces of Real Functions, Covers and Dense Subsets

Baire property of spaces of [0,1]-valued continuous functions

Mildly version of Hurewicz Basis covering property and Hurewicz measure zero spaces

Every metric space of weight λ=λℵ0​ admits a condensation onto a Banach space

Some observations on the mildly Menger property and topological games

Note on the Banach Problem 1 of condensations of Banach spaces onto compacta

Embedding Theorems for function spaces

Baire property of space of Baire-one functions

Various types of completeness in topologized semilattices

Topological properties of some function spaces

On homeomorphism groups and the set-open topology

On regular κ-bounded spaces admitting only constant continuous mappings into T1​ spaces of pseudo-character ≤κ

On Ramsey properties, function spaces, and topological games

Selectors for dense subsets of function spaces

Strongly sequentially separable function spaces, via selection principles

On the first Banach problem, concerning condensations of absolute $κ$ -Borel sets onto compacta

Baire property of spaces of $[0, 1]$ -valued continuous functions

Every metric space of weight $λ = λ^{ℵ_{0}}$ admits a condensation onto a Banach space

On regular $κ$ -bounded spaces admitting only constant continuous mappings into $T_{1}$ spaces of pseudo-character $\leq κ$