We find a set of conditions on a roof function to ensure topological mixing for suspension flows over a topological mixing base. In the measure theoretic case, such conditions have already been established for certain flows. Specifically, certain suspensions are topologically mixing if and only if the roof function is not cohomologous to a constant. We show that an analogous statement holds to establish topological mixing with the presence of dense periodic points. Much of the work required is to find properties specific to the equivalence class of functions cohomologous to a constant. In addition to these conditions, we show that the set of roof functions that induce a topologically mixing suspension is open and dense in the space of continuous roof functions.