Paper detail

Discretization of topological spaces

There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical sense) to compactification and give examples of discretizations. Especially, a discretization functor from the category of $α$-scattered Stonean spaces to the category of discrete spaces is constructed which is the converse of the Stone-Čech compactification functor. The interpretations of discretization in the level of algebras of functions are given.