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Essential completions of distributive lattices

Published online by Cambridge University Press:  17 April 2009

Gerhard Gierz  and
Albert R. Stralka
Gerhard Gierz
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521, U.S.A.
Albert R. Stralka
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521, U.S.A.
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Abstract

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The salient feature of the essential completion process is that for most common distributive lattices it will yield a completely distributive lattice. In this note it is shown that for those distributive lattices which have at least one completely distributive essential extension the essential completion is minimal among the completions by infinitely distributive lattices. Thus in its setting the essential completion of a distributive lattice behaves in much the some way as the one-point compactification of locally compact topological space does in its setting.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 3 , December 1985 , pp. 361 - 374
Copyright
Copyright © Australian Mathematical Society 1985

References

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