On generalized topological groups

TL;DR

This paper introduces generalized topological groups using a generalized topology framework, exploring their fundamental properties and connectedness, thus extending classical topological group theory.

Contribution

It defines and investigates the basic properties and connectedness of generalized topological groups, a novel extension of traditional topological groups.

Findings

Basic properties of generalized topological groups are established.

Connectedness properties of these structures are analyzed.

The work extends classical concepts to a generalized topological setting.

Abstract

In this work, we will introduce the notion of generalized topological groups using generalized topological structure and generalized continuity defined by ?A. Cs?asz?ar [2]. We will discuss some basic properties of this kind of structures and connectedness properties of this structures are given. Keywords: Generalized topology; generalized continuity; generalized topological groups; generalized connectedness.