On dual B-filters and dual B-subalgebras in a topological dual B-algebra

Abstract

This paper introduces the notion of the \(tdB\)-algebra, presents characteristics and properties of dual \(B\)-filters and dual \(B\)-subalgebras in a \(tdB\)-algebra, and introduces the uniform topology on a dual \(B\)-algebra in terms of its dual \(B\)-subalgebras. Moreover, this paper shows that a uniform dual \(B\)-structure is a \(tdB\)-algebra.