Geodesic
Proximity biframes and compactifications of completely regular ordered spaces
Theory and applications of categories, Tome 30 (2015), pp. 1469-1500.

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We generalize the concept of a strong inclusion on a biframe to that of a proximity on a biframe, which is related to the concept of a strong bi-inclusion on a frame introduced by Picado and Pultr. We also generalize the concept of a bi-compactification of a biframe to that of a compactification of a biframe, and prove that the poset of compactifications of a biframe L is isomorphic to the poset of proximities on L. As a corollary, we obtain Schauerte's characterization of bi-compactifications of a biframe. In the spatial case this yields Blatter and Seever's characterization of compactifications of completely regular ordered spaces and a characterization of bi-compactifications of completely regular bispaces.
Publié le :
Classification : 06D22, 54E55, 54D35, 54E05
Keywords: Frame, biframe, bispace, ordered space, compactification, proximity 
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     author = {Guram Bezhanishvili and Patrick J. Morandi},
     title = {Proximity biframes and
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     pages = {1469--1500},
     publisher = {mathdoc},
     volume = {30},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a43/}
}
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Guram Bezhanishvili; Patrick J. Morandi. Proximity biframes and
compactifications of completely regular ordered spaces. Theory and applications of categories, Tome 30 (2015), pp. 1469-1500. http://geodesic.mathdoc.fr/item/TAC_2015_30_a43/