On the bicompletion of a partial quasi-metric space and $$T_{0}$$-quasi-metric spaces

The purpose of the paper is to extend the completion theory of a partial metric space to the context of an asymmetric setup, namely, a partial quasi-metric space. We present two bicompletions of a partial quasi-metric space by appealing to the associated partial metric space on one hand and while on the other hand an associated $$T_{0}$$ -quasi-metric space is utilized. The two bicompletions are not necessarily the same but they coincide once the class of partial quasi-metric spaces considered is restricted to the class of $$T_{0}$$ -quasi-metric spaces.