Totally bounded frame quasi-uniformities
Fletcher, Peter ; Hunsaker, Worthen N. ; Lindgren, William F.
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 529-537 / Harvested from Czech Digital Mathematics Library
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This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity $\triangleleft $ 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 $\triangleleft $. The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum $\psi L$ and the compactification $\Re L$ of a uniform frame $(L, {\bold U})$ are meaningful for quasi-uniform frames. If ${\bold U}$ is a totally bounded quasi-uniformity on a frame $L$, there is a totally bounded quasi-uniformity $\overline{{\bold U}}$ on $\Re L$ such that $(\Re L, \overline{{\bold U}})$ is a compactification of $(L,{\bold U})$. Moreover, the Cauchy spectrum of the uniform frame $(Fr({\bold U}^{\ast }), {\bold U}^{\ast })$ can be viewed as the spectrum of the bicompletion of $(L,{\bold U})$.

Publié le : 1993-01-01
Classification:  06D20,  18B35,  54D35,  54E05,  54E15 
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     author = {Peter Fletcher and Worthen N. Hunsaker and William F. Lindgren},
     title = {Totally bounded frame quasi-uniformities},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {529-537},
     zbl = {0786.54028},
     mrnumber = {1243084},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118609}
}

Fletcher, Peter; Hunsaker, Worthen N.; Lindgren, William F. Totally bounded frame quasi-uniformities. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 529-537. http://gdmltest.u-ga.fr/item/118609/

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