On lattice-topological properties of general Wallman spaces
Let X be an arbitrary set and ℒ a lattice of subsets of X such that ϕ,X∈ℒ.𝒜(ℒ) is the algebra generated by ℒ and I(ℒ) consists of all zero-one valued finitely additive measures on 𝒜(ℒ). Various subsets of and I(ℒ) are considered and certain lattices are investigated as well as the topology of clos...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000039 |
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| Summary: | Let X be an arbitrary set and ℒ
a lattice of subsets of X such that ϕ,X∈ℒ.𝒜(ℒ) is the
algebra generated by ℒ and I(ℒ) consists of all zero-one valued finitely additive measures on
𝒜(ℒ). Various subsets of and I(ℒ) are considered and certain lattices are investigated as well as the topology of
closed sets generated by them. The lattices are investigated for normality, regularity, repleteness and
completeness. The topologies are similarly discussed for various properties such as
T2 and Lindelöf. |
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| ISSN: | 0161-1712 1687-0425 |