Constructing the sobrification of an approach space via bicompletion

Abstract

On every approach space X, we construct a compatible quasiuniform gauge structure which turns out to be at the same time the coarsest functorial structure and the nest compatible totally bounded one. Based on the analogy with the classical CsászárPervin quasi-uniform space, we call this the CsászárPervin quasi-uniform gauge space. By means of the bicompletion of this CsászárPervin quasi-uniform gauge space of a T0 approach space X, we succeed in constructing the sobrication of X.