A new characterization of Riemann-integrable functions

In this paper, we describe Riemann-integrable functions with the help of a new class of uniform functions. This description allows us to uncover the “countable” nature of the relation between the space of Riemann-integrable functions and the space of continuous functions. The argumentation is performed for any given topological space $T$ with limited Radon measure $\mu$ the support of which coincides with $T$.