A generalization of quasi-continuous functions and Riemann integration in refinement spaces

Two new properties are proven to be equivalent to the definition of quasi-continuous function. One of which is suitable for generalizing the definition to abstract spaces. Several properties of quasi-continuity in topological spaces are presented. Axioms are presented defining a refinement space in which several more properties of quasi-continuous functions are proven, and a Riemann type integral is defined in this space.