1. PROXIMITY BIFRAMES AND COMPACTIFICATIONS OF COMPLETELY REGULAR ORDERED SPACES.
- Author
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BEZHANISHVILI, GURAM and MORANDI, PATRICK J.
- Subjects
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FRAMES (Combinatorial analysis) , *COMPACTIFICATION (Mathematics) , *TOPOLOGICAL spaces , *PARTIALLY ordered sets , *ISOMORPHISM (Mathematics) - Abstract
We generalize the concept of a strong inclusion on a biframe [Sch93] to that of a proximity on a biframe, which is related to the concept of a strong bi-inclusion on a frame introduced in [PP12b]. We also generalize the concept of a bi-compactification of a biframe [Sch93] 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 [Sch93]. In the spatial case this yields Blatter and Seever's characterization of compactifications of completely regular ordered spaces [BS76] and a characterization of bi-compactifications of completely regular bispaces. [ABSTRACT FROM AUTHOR]
- Published
- 2015