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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.
@article{TAC_2015_30_a43,
author = {Guram Bezhanishvili and Patrick J. Morandi},
title = {Proximity biframes and
compactifications of completely regular ordered spaces},
journal = {Theory and applications of categories},
pages = {1469--1500},
publisher = {mathdoc},
volume = {30},
year = {2015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a43/}
}
TY - JOUR AU - Guram Bezhanishvili AU - Patrick J. Morandi TI - Proximity biframes and compactifications of completely regular ordered spaces JO - Theory and applications of categories PY - 2015 SP - 1469 EP - 1500 VL - 30 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2015_30_a43/ LA - en ID - TAC_2015_30_a43 ER -
%0 Journal Article %A Guram Bezhanishvili %A Patrick J. Morandi %T Proximity biframes and compactifications of completely regular ordered spaces %J Theory and applications of categories %D 2015 %P 1469-1500 %V 30 %I mathdoc %U http://geodesic.mathdoc.fr/item/TAC_2015_30_a43/ %G en %F TAC_2015_30_a43
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/