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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Hindawi Limited
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000744 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |