O. Sipacheva

activity

20242026

collaborators

5 papers

math.GN2026

Maximally almost periodic subgroups of elementary Abelian topological groups

Ol'ga Sipacheva

It is proved that any infinite elementary Abelian topological group has an infinite maximally almost periodic subgroup.

math.GN2026

Any countable topological $F_{p}$ -vector space has a closed discrete basis

Ol'ga Sipacheva

It is proved that any countable topological vector space over a finite field $F_{p}$ or, equivalently, any countable Abelian topological group of prime exponent has a closed…

math.GN2025

There are No Product and Subgroup Theorems for the Covering Dimension of Topological Groups

Ol'ga Sipacheva

Strongly zero-dimensional topological groups $G_{1}$ , $G_{2}$ , and $G$ such that $G_{1} \times G_{2}$ has positive covering dimension and $G$ contains a closed subgroup of positive covering…

math.GN2025

The completeness of free Boolean topological groups

Ol'ga V. Sipacheva, Mikhail G. Tkachenko

It is proved that the free Boolean topological group $B (X)$ on a Tychonoff space $X$ is Weil complete if and only if the space $X$ is DieudonnÃ© complete. This result provides a po…

math.GM2024

Free topological Mal'tsev algebras

Ol'ga V. Sipacheva, Aleksandr A. Solonkov

A brief introduction to universal algebra and the theory of topological algebras, their varieties, and free topological algebras is presented. Free topological Mal'tsev algebras ar…

Maximally almost periodic subgroups of elementary Abelian topological groups

Any countable topological Fp​-vector space has a closed discrete basis

There are No Product and Subgroup Theorems for the Covering Dimension of Topological Groups

The completeness of free Boolean topological groups

Free topological Mal'tsev algebras

Any countable topological $F_{p}$ -vector space has a closed discrete basis