A category of boolean algebras, a category of stonespaces and their duality

The main subject of this thesis is to give a direct formulation of famous Stone duality by making use of only the concept of equivalent functor. In addition to this, we extended the well-known equivalence between Boolean algebras and Boolean rings to a categorical isomorphism between categories of Boolean algebras and Boolean rings. In order to realize the main aim of the thesis, we have first established a functor from the opposite or category of Boolean algebras and Boolean homomorphisms and the category of Stone spaces and continuous functions, and then shown that such a functor is an equivalence. In particular, the formulation of Stone duality, in this thesis differs from the existing approach in the literature in such a way that the present thesis relies on only the definition of equivalent functor.