A. Karassev

activity

20082025

most citedOn homotopical and homological

Z_{n}

-sets

4 citations · 7 across the 10 of their papers we have counts for

collaborators

12 papers

math.RA2025

Simple polynomial equations over (mxm)-matrices

Vitalij A. Chatyrko, Alexandre Karassev

Let $m$ be any integer $\geq 3$ . We consider the polynomial equation $X^{n} + a_{n - 1} \cdot X^{n - 1} + \dots + a_{1} \cdot X + a_{0} \cdot I = O,$ over $(m \times m)$ -matrices $X$ with t…

math.RA2025

Simple polynomial equations over $(2 \times 2)$ -matrices

Vitalij A. Chatyrko, Alexandre Karassev

We consider the polynomial equation $X^{n} + a_{n - 1} \cdot X^{n - 1} + \dots + a_{1} \cdot X + a_{0} \cdot I = O,$ over $(2 \times 2)$ -matrices $X$ with the real entries, where $I$ is the…

math.GN2025

On structural numbers of topological spaces

Vitalij Chatyrko, Alexandre Karassev

Zero-dimensional structural numbers $Z_{0}^{ind}$ and $Z_{0}^{dim}$ w.r.t. dimensions $ind$ and $dim$ were introduced by Georgiou, Hattori, Megariti…

math.GN2024

From homogeneity to discrete homogeneity

Vitalij A. Chatyrko, Alexandre Karassev

This is a survey of recent and classical results concerning various types of homogeneity, such as n-homogeneity, discrete homogeneity, and countable dense homogeneity. Some new res…

math.GN2023

On generalized $V^{n}$ -continua

A. Karassev, P. Krupski, V. Todorov +1

The notion of a $V^{n}$ -continuum was introduced by Alexandroff \cite{ps} as a generalization of the concept of $n$ -manifold. In this note we consider the cohomological analogue of $…

math.GN2023

Homogeneous spaces not separated by arcs

Alexandre Karassev, Vesko Valov

It was shown by van Mill and Valov that regions in strongly locally homogeneous locally compact metric spaces of dimension $\geq 2$ are not separated by arcs. We improve this result…

Simple polynomial equations over (mxm)-matrices

Simple polynomial equations over (2×2)-matrices

On structural numbers of topological spaces

From homogeneity to discrete homogeneity

On generalized Vn-continua

Homogeneous spaces not separated by arcs

Simple polynomial equations over $(2 \times 2)$ -matrices

On generalized $V^{n}$ -continua