On the extension of classes of continuous maps to the bicompletion in quasi-uniform spaces

Abstract

In [6] characterizations of continuous maps between uniform spaces in terms of nets and filters are provided. Also, extensions of maps defined on a dense subset of a uniform space that preserve Cauchy filterbases between uniform spaces to the whole space are discussed. It is the purpose of this paper to extend some of these results to the setting of quasi-uniform spaces, by discussing extensions of maps that preserve Cauchy filterbases between quasi-uniform spaces to the bicompletion. We also show that some results in [3] concerning extensions of quasi-uniformly continuous maps from T 1-half completable quasi-uniform spaces also hold for maps that preserve Cauchy filterbases.