Embedding into connected, locally connected topological gyrogroups

TL;DR

This paper proves that every topological gyrogroup can be embedded into a connected, locally connected topological gyrogroup, enhancing understanding of their structure and relationships.

Contribution

It introduces a method to embed any topological gyrogroup into a connected, locally connected one, establishing a significant structural connection.

Findings

Every topological gyrogroup is isomorphic to a closed subgyrogroup of a connected, locally connected topological gyrogroup.

The embedding preserves topological and algebraic structures.

Provides a new perspective on the structure of topological gyrogroups.

Abstract

In this paper, it is proved that every topological gyrogroup $G$ is topologically groupoid isomorphic to a closed subgyrogroup of a connected, locally connected topological gyrogroup $G^{\bullet}$.