Free topological Mal'tsev algebras

TL;DR

This paper explores the properties and relationships of free topological Mal'tsev algebras within the context of universal algebra and topological algebra, including their connection to topological groups and heaps.

Contribution

It provides new insights into the structure and decomposition of free topological Mal'tsev algebras, linking them to other algebraic structures.

Findings

Analysis of properties of free topological Mal'tsev algebras

Relationship established with topological groups and heaps

Discussion on the problem of direct limit decomposition

Abstract

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 are studied. Their properties, relationship with topological groups and heaps, and the problem of direct limit decomposition are considered.