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 $��$-scattered Stonean spaces to the category of discrete spaces is constructed which is the converse of the Stone-��ech compactification functor. The interpretations of discretization in the level of algebras of functions are given.

19 pages