Normal lattices and coseparation of lattices

Let X be an arbitrary non-empty set, and let ℒ be a lattice of subsets of X such that ∅, X∈ℒ. We first summarize a number of known conditions which are equivalent to ℒ being normal. We then develop new equivalent conditions in terms of set functions associated with μ∈I(ℒ), the set of all non-trivial...

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Main Author:	Barry B. Mittag
Format:	Article
Language:	English
Published:	Hindawi Limited 1997-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	normal lattice coseparation of lattices zero-one valued measures associated outer measures.
Online Access:	http://dx.doi.org/10.1155/S0161171297000744

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spelling	doaj-66c8ffc52c9d4e90bbcde68c6d7f39b62020-11-24T23:30:06ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120355355910.1155/S0161171297000744Normal lattices and coseparation of latticesBarry B. Mittag0Department of Mathematics, Sacred Heart University, 5151 Park Avenue, Fairfield 06432-1000, CT, USALet X be an arbitrary non-empty set, and let ℒ be a lattice of subsets of X such that ∅, X∈ℒ. We first summarize a number of known conditions which are equivalent to ℒ being normal. We then develop new equivalent conditions in terms of set functions associated with μ∈I(ℒ), the set of all non-trivial, zero-one valued finitely additive measures on the algebra generated-by ℒ′. We finally generalize all the above to the situation where ℒ1 and ℒ2 are a pair of lattices of subsets of X with ℒ′1⊂ℒ2, and where we obtain equivalent conditions for ℒ1 to coseparate ℒ2.http://dx.doi.org/10.1155/S0161171297000744normal latticecoseparation of latticeszero-one valued measures associated outer measures.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Barry B. Mittag
spellingShingle	Barry B. Mittag Normal lattices and coseparation of lattices International Journal of Mathematics and Mathematical Sciences normal lattice coseparation of lattices zero-one valued measures associated outer measures.
author_facet	Barry B. Mittag
author_sort	Barry B. Mittag
title	Normal lattices and coseparation of lattices
title_short	Normal lattices and coseparation of lattices
title_full	Normal lattices and coseparation of lattices
title_fullStr	Normal lattices and coseparation of lattices
title_full_unstemmed	Normal lattices and coseparation of lattices
title_sort	normal lattices and coseparation of lattices
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1997-01-01
description	Let X be an arbitrary non-empty set, and let ℒ be a lattice of subsets of X such that ∅, X∈ℒ. We first summarize a number of known conditions which are equivalent to ℒ being normal. We then develop new equivalent conditions in terms of set functions associated with μ∈I(ℒ), the set of all non-trivial, zero-one valued finitely additive measures on the algebra generated-by ℒ′. We finally generalize all the above to the situation where ℒ1 and ℒ2 are a pair of lattices of subsets of X with ℒ′1⊂ℒ2, and where we obtain equivalent conditions for ℒ1 to coseparate ℒ2.
topic	normal lattice coseparation of lattices zero-one valued measures associated outer measures.
url	http://dx.doi.org/10.1155/S0161171297000744
work_keys_str_mv	AT barrybmittag normallatticesandcoseparationoflattices
_version_	1725542952369913856

Normal lattices and coseparation of lattices

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