Pointwise Quasi uniformities on Completely Distributive Lattices

Abstract:

      In this paper we introduced a new theory of pointwise quasi-uniformities on completely distributive lattices. We prove theorems corresponding to many of the usual theorems. In particular we show every topological moiecullar lat-tice is quasi - uniformitizable and every quasi-uniformly contiuous GOH is conti-uous. We also show that' for every quasi uniformity u, there is the finest quasi-uniformity in [u], where [u]={φ:φ has the same induced COT topology as u},and wealso give the structure of the finest quasi-uniformity.