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