Reciprocally Determining of Quasi-uniformities and Quasi-proximities
Hu Zhao · Neimenggu Shi-da xuebao. Zhexue shehui kexue hanwen ban · 2011
In this paper,it is proved that,for a given set X,an appropriate partial order can be defined on QP(X)(the set of all Quasi-proximities on the set X),such that(QP(X),) is a complete lattice which is isomorphic with(TQU(X),)(the set of all totally bounded Quasi-uniformities on X).Thus a quasi-proximities on a set X can be determined by a totally bounded Quas-uniformity.