Evgenii Reznichenko

collaborators

6 papers

math.GN2026

When are metrizable linear subspaces of topological vector spaces finite-dimensional?

Vladislav V. Maksimov, Evgenii A. Reznichenko

We study conditions that imply finite-dimensionality of metrizable or Frechet-Urysohn linear subspaces of topological vector spaces (TVS). We consider the classes $D_{M}$ a…

math.FA2026

Locally convex spaces with hemicompact weak* dual

Evgenii Reznichenko

For a locally convex space $L$ let $L_{σ}^{'}$ denote its dual endowed with the weak* topology $σ (L^{'}, L)$ . We prove that $L_{σ}^{'}$ is hemicompact if and only if $L$ with the Mackey topology…

math.GN2026

Hemicompactness and the $k_{ω}$ -property of free topological vector spaces

Evgenii Reznichenko

For a Tychonoff space $X$ we consider the vector space $E (X)$ with basis $X$ endowed with one of the following topologies: the weak topologies $L_{b} (X)$ and $L_{p} (X)$ generated by $C…

math.GN2026

Metrizable and Fréchet--Urysohn subgroups and linear subspaces of topological vector spaces

Arkady Leiderman, Evgenii Reznichenko, Ol'ga Sipacheva

For a normed space $E$ , we denote by $E_{w}$ and $E_{w^{*}}^{'}$ the space $E$ and its dual $E^{'}$ endowed with the weak topology $w$ and the weak $^{*}$ topology $w^{*}$ , respectively. It is we…

math.GN2026

$ϰ$ -Fréchet--Urysohn and Baire subgroups of free topological groups

Arkady Leiderman, Evgenii Reznichenko, Ol'ga Sipacheva

A topological space is $ϰ$ -Fréchet--Urysohn if every point in the closure of an open set $U$ is the limit of a sequence of points of $U$ . We prove that every $ϰ$ -Fr…

math.GN2025

Weird $R$ -Factorizable Groups

Evgenii Reznichenko, Ol'ga Sipacheva

The problem of the existence of non-pseudo- $ℵ_{1}$ -compact $R$ -factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger th…

When are metrizable linear subspaces of topological vector spaces finite-dimensional?

Locally convex spaces with hemicompact weak* dual

Hemicompactness and the kω​-property of free topological vector spaces

Metrizable and Fréchet--Urysohn subgroups and linear subspaces of topological vector spaces

ϰ-Fréchet--Urysohn and Baire subgroups of free topological groups

Weird R-Factorizable Groups

Hemicompactness and the $k_{ω}$ -property of free topological vector spaces

$ϰ$ -Fréchet--Urysohn and Baire subgroups of free topological groups

Weird $R$ -Factorizable Groups