2022-02-032022-02-03197213673542https://hdl.handle.net/10657/8665Two 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.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital