Normal Subgroups and Quotient Groups in β-α-topological Group

Hariwan Z. Ibrahim , Alias B. Khalaf

In this paper, we studied the subgroup in β-α-topological group and several basic theorems are introduced. From normal subgroups, the study naturally follows to quotient groups, which are decomposition spaces topologically. The quotient group space of β-α-topological groups defined ...

Topological Group Via Operations defined on α-Open Sets

Hariwan Z. Ibrahim , Alias B. Khalaf

In this paper, we begin the study of β-α-continuous multiplication map. Here we begin by stating some properties of β-α-continuous multiplication and define the β-α-continuity of the inversion map as well. We then introduce the concept of β-α-topological groups ...