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Completion of lattices of semi-continuous functions

Published online by Cambridge University Press:  09 April 2009

John August
Affiliation:
Frostburg State CollegeFrostburg, Maryland 21532, U.S.A.
Charles Byrne
Affiliation:
The Catholic University of AmericaWashington, D.C. 20064, U.S.A.
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Abstract

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If U and V are toplogies on an abstract set x, then the triple (X, U, V) is a bitopologica space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued functions on certain bitopological spaces. The distributivity of certain lattices is investigated, and the theorem of Funayama on distributive normal completions is generalized.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1978

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