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  • Author or Editor: H. Künzi x
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W prov that if the quasi-proximity class of a quasi-uniformity poss ss s mor than on member, th n it contains at least 2 2 .0 members.

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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 T 0-refiection of the Hausdorff quasi-uniformity of a quasiuniform space.

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