A. Lipin

activity

20232026

most citedAdversarial Synchronization

1 citations · 1 across the 9 of their papers we have counts for

collaborators

10 papers

math.GN2026

Homogeneous linearly ordered spaces

Anton Lipin, Evgenii Reznichenko

Every compact subset of a homogeneous generalized ordered (GO) space has character at most $ω_{1}$ and cardinality at most $2^{ω_{1}}$ ; if such a subset has uncountable character, then…

cs.FL2026★ 1 cited

Adversarial Synchronization

Anton E. Lipin, Mikhail V. Volkov

We study a variant of the synchronization game on finite deterministic automata. In this game, Alice chooses one input letter of an automaton $A$ on each of her moves while Bob may…

math.GN2025

Resolvability in products of spaces of small cardinality

Anton Lipin

We prove that: I. The product of any two regular isodyne spaces of cardinality $ω_{1}$ is $ω$ -resolvable; II. The product of any $n + 2$ Hausdorff isodyne spaces of cardinality $ω_{n}$ …

math.GN2025

$R^{ω_{1}}$ -Factorizable Spaces and Groups

Anton Lipin, Evgenii Reznichenko, Ol'ga Sipacheva

A topological space $X$ is $R^{ω_{1}}$ -factorizable if any continuous function $f : X \to R^{ω_{1}}$ factors through a continuous function from $X$ to a second-count…

math.GN2025

Resolvability in products and squares

Anton Lipin

Suppose $X$ and $Y$ are topological spaces, $∣ X ∣ = Δ (X)$ and $∣ Y ∣ = Δ (Y)$ . We investigate resolvability of the product $X \times Y$ . We prove that: I. If $∣ X ∣ = ∣ Y ∣ = ω$ and $X, Y$ …

math.GN2024

Relatively functionally countable subsets of products

Anton Lipin

A subset $A$ of a topological space $X$ is called relatively functionally countable (RFC) in $X$ , if for each continuous function $f : X \to R$ the set $f [A]$ is countable…

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

On resolvability and tightness in uncountable spaces

Anton Lipin

We investigate connections between resolvability and different forms of tightness. This study is adjacent to [1,2]. We construct a non-regular refinement $τ^{*}$ of the natural topol…

math.GN2023

On resolvability, connectedness and pseudocompactness

Anton Lipin

We prove that: I. If $L$ is a $T_{1}$ space, $∣ L ∣ > 1$ and $d (L) \leq κ \geq ω$ , then there is a submaximal dense subspace $X$ of $L^{2^{κ}}$ such that $∣ X ∣ = Δ (X) = κ$ ; II. If $\frak{c}\leqκ…

math.GN2023

Resolvability and complete accumulation points

A. E. Lipin

We prove that: I. For every regular Lindelöf space $X$ if $∣ X ∣ = Δ (X)$ and $cf ∣ X ∣ \neq = ω$ , then $X$ is maximally resolvable; II. For every regular countably compact space $X$ i…

Homogeneous linearly ordered spaces

Adversarial Synchronization

Resolvability in products of spaces of small cardinality

Rω1​-Factorizable Spaces and Groups

Resolvability in products and squares

Relatively functionally countable subsets of products

Tightness type properties of spaces of quasicontinuous functions

On resolvability and tightness in uncountable spaces

On resolvability, connectedness and pseudocompactness

Resolvability and complete accumulation points

$R^{ω_{1}}$ -Factorizable Spaces and Groups