The Scale of a Quasi-uniform Space
(Sprache: Englisch)
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...
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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.
Bibliographische Angaben
- Autor: Olivier Olela Otafudu
- 2010, 92 Seiten, Kartoniert (TB), Englisch
- Verlag: LAP Lambert Academic Publishing
- ISBN-10: 3843385629
- ISBN-13: 9783843385626
Sprache:
Englisch
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