We give a new completion for the quasi-uniform spaces. We call the whole procedure { \it $\tau$-completion} and the new space { \it $\tau$-complement of the given}. The basic result is that every $T_{ _0}$ quasi-uniform space has a $\tau$-completion. The $\tau$-complement has some \textquotedblleft crucial\textquotedblright properties, for instance, it coincides with the classical one in the case of uniform space or it extends the { \it Doitcinov's completion for the quiet spaces}. We use nets and from one point of view the technique of the construction may be considered as a combination of the { \it Mac Neille's cut} and of the completion of partially ordered sets via { \it directed subsets}.
Categories: math.GN