Extension closed properties on generalized topological groups

Murad Hussain,Moiz Ud Din Khan,Ahmet Zemci Özcelik,Cenap Özel

doi:10.1007/s40065-014-0102-9

Murad Hussain, Moiz Ud Din Khan + Show 2 more

Open Access

https://doi.org/10.1007/s40065-014-0102-9

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Abstract

In this paper, we continue to investigate some important results in generalized topological groups and we prove extension closed property for connectedness, compactness, and separability of generalized topological groups. Last, we define generalized topological group actions on generalized topological spaces and we establish a homeomorphism between action group and action space.

Highlights

In [2], Császár introduced and extensively studied the notion of generalized open sets discarding finite intersection axiom from the general topology
In [8], we defined the generalized topological group structure and we proved some basic results
We continue to investigate some important results in generalized topological groups and prove extension closed property for connectedness, compactness, first countability and separability of generalized topological groups

Summary

Introduction

In [2], Császár introduced and extensively studied the notion of generalized open sets discarding finite intersection axiom from the general topology. Theorem 2.5 The G-quotient mapping π of G onto the G-quotient space G/H is G-perfect where H is a G-compact subgroup of a G-ultra Hausdorff normal G-topological group G. Corollary 2.6 Let H be a G-compact subgroup of a G-ultra Hausdorff normal G-topological group G such that the G-quotient space G/H is G-compact.

Results

Conclusion