View More View Less
  • 1 University of Cape Town Department of Mathematics and Applied Mathematics Rondebosch 7701 South Africa
Restricted access

Abstract  

We investigate the left-sided scale and the two-sided scale of a quasi-uniform space. While the two-sided scale of a quasi-uniform space X shows a behavior similar to the usual hyperspace of X equipped with its Hausdorff quasiuniformity, the left-sided scale generalizes the quasi-uniform multifunction space of X into itself. Either construction of the scale relies on the concept of the prefilter space of a quasi-uniform space. Prefilter spaces of quasi-uniform spaces are proved to be bicomplete. Consequently both the left-sided and the two-sided scale of a quasiuniform space are bicomplete. Indeed these scales can be used to construct the bicompletion of the T0-refiection of the Hausdorff quasi-uniformity of a quasiuniform space.