Completion of pre-quasi-uniform spaces

The purpose in this paper is to prove the existence of a canonical-pre-quasi-uniform extension (X,U)ˆ of a pre-quasi-uniform space (X,U). Most of the concepts used in quasi-uniform spaces may be applied to pre-quasi-uniform spaces. These spaces were introduced by the first author and developed by the second in his doctoral thesis. We shall study the main properties of this class of spaces which contains the class of quasi-uniform spaces.