A Note on Some Unified Types of Open and Locally Closed Sets

Zanyar A. Ameen , Baravan A. Asaad

Recently, new types of (open) sets have been studied by some topologists. This note shows that these sets are identical to some other sets already exist in the literature.

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 ...