A theory of discrete analysis
In a previous paper the author characterized Lipschitz mappings in terms of sequences of finite variation. By using this characterization, in the present paper a discrete analysis is developed which is a purely algebraic construction. The major constructions in discrete analysis are: discrete differential structures, the integral envelope and the integral completion. It is shown that the space of real numbers is the integral completion of rational numbers and the space of all complex periodic distributions is the integral completion of the class of infinitely differentiable periodic functions.
scientific article; zbMATH DE number 167995