Alexander V. Osipov

activity

20232026

collaborators

8 papers

math.GN2026

On properties close to Polish cofinality in spaces of Baire-one and continuous functions

Alexander V. Osipov

In this paper we prove that $B_{1} (X)$ has a dense cofinally Polish subspace if and only if $X$ is a $Δ_{1}$ -space. Also we prove that $B_{1} (X, [0, 1])$ has a dense cofinally Polish subs…

math.GN2026

Some function applications of weak $λ$ -spaces

Alexander V. Osipov

In this paper it is proved that there exists (in $Z F C$ ) a separable pseudocompact weak $λ$ -space $X$ which is not $Δ_{1}$ -space. It follows that there exists a space $X$ such that $B…

math.GN2024

On Baire property of spaces of compact-valued measurable 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.GN2024

Velichko's notions close to sequentially separability and their hereditary variants in $C_{p}$ -theory

Alexander V. Osipov

A space $X$ is sequentially separable if there is a countable $S \subset X$ such that every point of $X$ is the limit of a sequence of points from $S$ . In 2004, N.V. Velichko define…

math.GN2024

Tightness type properties of spaces of quasicontinuous functions

Anton E. Lipin, Alexander V. Osipov

Using approximation by continuous functions we prove the following statements to types of tightness in a space $Q_{p} (X, R)$ of all quasicontinuous real-valued functions wit…

math.GN2024

Dieudonné completeness of function spaces

Mikhail Al'perin, Alexander V. Osipov

A space is called Dieudonné complete if it is complete relative to the maximal uniform structure compatible with its topology. In this paper, we investigated when the function spac…

math.GN2023

On the product of almost discrete Grothendieck spaces

Alexander V. Osipov

A topological space $X$ is called almost discrete, if it has precisely one nonisolated point. In this paper, we get that for a countable product $X = \prod X_{i}$ of almost discrete sp…

math.GN2023

On countable tightness type properties of spaces of quasicontinuous functions

Alexander V. Osipov

In this paper we get characterizations countable tightness, countable fan-tightness and countable strong fan-tightness of spaces of quasicontinuous functions with the topology of p…

On properties close to Polish cofinality in spaces of Baire-one and continuous functions

Some function applications of weak λ-spaces

On Baire property of spaces of compact-valued measurable functions

Velichko's notions close to sequentially separability and their hereditary variants in Cp​-theory

Tightness type properties of spaces of quasicontinuous functions

Dieudonné completeness of function spaces

On the product of almost discrete Grothendieck spaces

On countable tightness type properties of spaces of quasicontinuous functions

Some function applications of weak $λ$ -spaces

Velichko's notions close to sequentially separability and their hereditary variants in $C_{p}$ -theory