Abstract
A weak form of weak quasi-continuity, which we call subweak quasi-continuity, is introduced. It is shown that subweak quasi-continuity is strictly weaker than weak quasi-continuity. Subweak quasi-continuity is used to strengthen several results in the literature concerning weak quasi-continuity. Specifically, results concerning the graph, graph function, and restriction of a weakly quasi-continuous function are extended slightly. Also, a result concerning weakly quasi-continuous retractions is strengthened.