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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Interposition and lattice cones of functions


Authors: Jörg Blatter and G. L. Seever
Journal: Trans. Amer. Math. Soc. 222 (1976), 65-96
MSC: Primary 46E05; Secondary 54E05, 41A65
MathSciNet review: 0438094
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Abstract: A lattice cone of functions on a set X is a convex cone of bounded real-valued functions on X which contains the constants and which is closed under the lattice operations. Our principal results concern the relation between closed lattice cones on a set X and certain binary relations, called inclusions, on the power set of X. These results are applied to interposition problems, Császár compactifications of quasi-proximity spaces, the compactification of Nachbin's completely regular ordered topological spaces, and a problem in best approximation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0438094-0
PII: S 0002-9947(1976)0438094-0
Keywords: Lattice cone, inclusion, interposition, quasi-proximity, ordered topological space, quasi-proximity compactification, ordered topological space compactification, best approximation
Article copyright: © Copyright 1976 American Mathematical Society