Groups of Invertible Binary Operations of a Topological Space

TL;DR

This paper investigates continuous binary operations on topological spaces, providing criteria for invertibility, classifying invertible groups in certain spaces, and establishing a theorem on binary distributive representations of topological groups.

Contribution

It introduces a criterion for invertibility of continuous binary operations and classifies invertible groups in locally compact, locally connected spaces, along with a new theorem on binary distributive representations.

Findings

Criteria for invertibility of binary operations established

Classification of invertible groups in specific topological spaces completed

A new theorem on binary distributive representation proved

Abstract

In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible continuous binary operations of locally compact and locally connected spaces is solved. A theorem on the binary distributive representation of a topological group is also proved.