We continue our investigations of the scale of a quasi-uniform space, which we had started in an earlier article. We distinguish between the left-sided scale and the two-sided scale of a quasi-uniform space. While the behavior of the two-sided scale of a quasi-uniform space X shows similarities with the usual hyperspace of X equipped with its Hausdorff quasi-uniformity, the left-handed scale generalizes the quasi-uniform multifunction space of X into itself.For instance the two-sided scale of any totally bounded quasi-uniform space X is totally bounded, while total boundedness of the left-sided scale of a quasi-uniform space X implies that X is finite or indiscrete. Either construction of the scale is based on the idea of the prefilter space of a quasi-uniform space. Prefilter spaces of quasi-uniform spaces are shown to be bicomplete. It follows that both the left-sided and the two-sided scale of a quasi-uniform space are bicomplete. Indeed these scales can be used to construct the bicompletion of the T0-reflection of the Hausdorff quasi-uniformity of a quasi-uniform space.
|Author||Olivier Olela Otafudu|
|Number of Pages||92|
|Country of Manufacture||India|
|Product Brand||LAP LAMBERT Academic Publishing|
|Product Packaging Info||Box|
|In The Box||1 Piece|
|Product First Available On ClickOnCare.com||2015-07-25 00:00:00|