A. Lipin

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20242026

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math.GN2026

Resolvability in products of spaces of small cardinality

Anton Lipin

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

math.GN2026

$R^{I ¨ _{1}}$ -Factorizable Spaces and Groups

Anton Lipin, Evgenii Reznichenko, Ol'ga Sipacheva

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

math.GN2025

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 $I ¨ ^{*}$ of the natural topo…

math.GN2025

Resolvability in products and squares

Anton Lipin

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

math.GN2025

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

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…

Resolvability in products of spaces of small cardinality

RI¨1​-Factorizable Spaces and Groups

On resolvability and tightness in uncountable spaces

Resolvability in products and squares

Tightness type properties of spaces of quasicontinuous functions

Relatively functionally countable subsets of products

$R^{I ¨ _{1}}$ -Factorizable Spaces and Groups