Reflectional topology in MV-algebras

In this paper, we define soaker ideals in an MV-algebra, and study the relationships between soaker ideals and the other ideals in an involutive MV -algebras. Then we introduce a topology on the set of all the soaker ideals, which we call reflectional topology, and give a basis for it. By defining the notion of join-soaker ideals, we show that the reflectional topology is compact. We also give a characterization of connectedness of the reflectional topology. Finally, we investigate the properties of T۰ and T۱-space in this topology.

Keywords:

Finitely meet-irreducible , involutive , (soaker , join-soaker) ideal , reflectional topology