Weak bases and quasi-pseudo-metrization of bispaces

In this paper it is obtained a quasi-pseudo-metrization theorem which provides a certain unification in the treatment of the biquasi-metrization problem when it is considered via sequences of neighborhoods of each point satisfying certain properties. In particular, the well-known theorems of Fox, Raghavan, Künzi, and Raghavan and Reilly are deduced from our results. We also obtain some quasi-metrization theorems in terms of pairwise locally symmetric bifunctions.