On structure of topological metagroups

TL;DR

This paper explores the topological structures of metagroups, examining their properties, homomorphisms, quotient maps, and complex constructions like smashed products and wreath products, with implications for generalized $C^*$-algebras.

Contribution

It provides a detailed analysis of topological metagroups, including their structure, homomorphisms, quotient maps, and complex product constructions, advancing understanding in this mathematical area.

Findings

Topologies on metagroups are characterized.

Homomorphisms and quotient maps are systematically studied.

Smashed products and wreath products form topological metagroups.

Abstract

In this article topologies on metagroups are studied. They are related with generalized $C^*$-algebras over ${\bf R}$ or ${\bf C}$. Homomorphisms and quotient maps on them are investigated. Structure of topological metagroups is scrutinized. In particular, topologies on smashed products and smashed twisted wreath products of metagroups are scrutinized, which are making them topological metagroups. Moreover, their inverse homomorphism systems are studied.