Constructing new Segal topological algebras from existing ones

In this paper, we examine the properties of Segal topological algebras, looking at ways to construct new objects from existing ones. Equipped with the example of algebras (in the sense of vector spaces equipped with multiplication), we consider two approaches: one via a direct product of an arbitrary family of Segal topological algebras and another using the Dorroh extensions of the underlying topological algebras.