In this paper j a new theory on poilitwise quasi-uniformity is based on completelydistributive lattices.Properties of closure,locally basis, continuity etc.are discussed in inducedtopological molecular lattices. EaCh tOPological molecular lattice can be induced by a pot￣isequasi-whfondty.Moreover,an equldsnt definition and a characterization of pseudDequasimetric in [8]are given.P seudth quas i- metrization theorem is obt anied.