Normal characterizations of lattices
Let X be an arbitrary nonempty set and ℒ a lattice of subsets of X such that ∅, X∈ℒ. Let 𝒜(ℒ) denote the algebra generated by ℒ and I(ℒ) denote those nontrivial, zero-one valued, finitely additive measures on 𝒜(ℒ). In this paper, we discuss some of the normal characterizations of lattices in terms o...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201007256 |
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| Summary: | Let X be an arbitrary nonempty set and ℒ a lattice of subsets of X such that ∅, X∈ℒ. Let 𝒜(ℒ) denote the algebra generated by ℒ and I(ℒ) denote those nontrivial, zero-one valued, finitely additive
measures on 𝒜(ℒ). In this paper, we discuss some of the normal characterizations of lattices in terms of the associated lattice regular measures, filters and outer measures. We consider
the interplay between normal lattices, regularity or σ-smoothness properties of measures, lattice topological properties and filter correspondence. Finally, we start a study of slightly, mildly and strongly normal lattices and express then some of these results in terms of the generalized Wallman spaces. |
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| ISSN: | 0161-1712 1687-0425 |