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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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000744 |
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| _version_ | 1850158909734518784 |
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| author | Barry B. Mittag |
| author_facet | Barry B. Mittag |
| author_sort | Barry B. Mittag |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-66c8ffc52c9d4e90bbcde68c6d7f39b6 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-66c8ffc52c9d4e90bbcde68c6d7f39b62025-08-20T02:23:44ZengWileyInternational 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. |
| 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. |
| title | 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_short | Normal lattices and coseparation of lattices |
| title_sort | normal lattices and coseparation of lattices |
| 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 |