{"product_id":"the-scale-of-a-quasi-uniform-space-von-olivier-olela-otafudu","title":"The Scale of a Quasi-uniform Space","description":"\u003cp\u003eWe 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783843385626\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783843385626","offer_id":39497188016221,"sku":"9783843385626","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/47cd643f-4fa7-4191-885a-80280a8e5e6e.jpg?v=1757656418","url":"https:\/\/shop.autorenwelt.de\/products\/the-scale-of-a-quasi-uniform-space-von-olivier-olela-otafudu","provider":"Autorenwelt Shop","version":"1.0","type":"link"}