Totally bounded frame quasi-uniformities
نویسندگان
چکیده
This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity ⊳ on a frame L there is a totally bounded quasi-uniformity on L that is the coarsest quasi-uniformity, and the only totally bounded quasi-uniformity, that determines ⊳. The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum ψL and the compactification RL of a uniform frame (L,U) are meaningful for quasi-uniform frames. If U is a totally bounded quasi-uniformity on a frame L, there is a totally bounded quasi-uniformity U on RL such that (RL,U) is a compactification of (L,U). Moreover, the Cauchy spectrum of the uniform frame (Fr(U),U) can be viewed as the spectrum of the bicompletion of (L,U).
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