2010/08/08 by Athanasios Andrikopoulos, Andrikopoulos, Athanasios, John Stabakis +1
Mathematics · #FOS: Mathematics #General Topology (math.GN) #math.GN
paper · pdf · doi:10.48550/arxiv.1008.1402
arxiv created 2010/08/08 · arxiv updated 2010/08/10
We give a new completion for the quasi-uniform spaces. We call the whole procedure \it τ-completion and the new space \it τ-complement of the given. The basic result is that every T0 quasi-uniform space has a τ-completion. The τ-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.