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Completion of lattices of semi-continuous functions

Published online by Cambridge University Press:  09 April 2009

John August  and
Charles Byrne
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
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 4 , December 1978 , pp. 453 - 464
Copyright
Copyright © Australian Mathematical Society 1978

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