The Scale of a Quasi-uniform Space

 
9783843385626: The Scale of a Quasi-uniform Space

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.

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As in others fields of Mathematical sciences, symmetry plays an essential role in computer science. However, in many applications one has to deal with incomplete information and this often implies that asymmetry is unavoidable.

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Book Description LAP Lambert Academic Publishing, Germany, 2010. Paperback. Book Condition: New. 220 x 150 mm. Language: English . Brand New Book ***** Print on Demand *****.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. Bookseller Inventory # AAV9783843385626

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Book Description LAP LAMBERT Academic Publishing. Paperback. Book Condition: New. Paperback. 92 pages. Dimensions: 8.7in. x 5.9in. x 0.2in.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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Bookseller Inventory # 9783843385626

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