Michael Megrelishvili

activity

20242026

collaborators

5 papers

math.GN2026

Intrinsic uniform structure on median algebras

Michael Megrelishvili

We introduce the median uniformity $U_{m}$ , an intrinsic precompact convex uniform structure on a median algebra. It is Hausdorff under natural assumptions, for in…

math.DS2026

Tameness of actions on finite rank median algebras

Michael G. Megrelishvili

We show that for every finite-rank median algebra $X$ , the rank of $X$ coincides with the independence number of the family of all median-preserving maps $X \to [0, 1]$ . In the comp…

math.GN2025

Circular orders: topology and continuous actions

Michael Megrelishvili

We study the topology of circularly ordered sets. While the algebraic notion is classical, the general topological theory has received comparatively little attention. In this work…

math.DS2024

Key subgroups in the Polish group of all automorphisms of the rational circle

Michael Megrelishvili

Extending some results of a joint work with E. Glasner, we continue to study the Polish group $G := Aut (Q_{0})$ of all circular order preserving permutations of the r…

math.FA2024

Lipschitz-Free Spaces: A Topometric Approach and Group Actions

Michael Megrelishvili

We introduce a topometric version of Lipschitz-free spaces and study its universal property. Another aim of this paper is to investigate actions of topological groups $G$ on Lipsch…