Point classes of compactifications of discrete spaces

We consider the compactification of one countable discrete space. This compactification is constructed as the Stone space of some Boolean algebra. We obtained some classes of points of remainder of this space, found dependence to the closures of countable subsets of these classes and also proved the existence of subsets of remainder whose closures are homeomorphic to a minimal (one-point) compactification of a countable discrete space, and subsets whose closure is homeomorphic to the Stone–Ĉzech space. We considered other properties of this space.