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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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171298000039 |
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| _version_ | 1832563594513874944 |
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| author | Carmen Vlad |
| author_facet | Carmen Vlad |
| author_sort | Carmen Vlad |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d0fe5d050da246a8a730381172a1e692 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d0fe5d050da246a8a730381172a1e6922025-02-03T01:13:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-01211253210.1155/S0161171298000039On lattice-topological properties of general Wallman spacesCarmen Vlad0Mathematics Department, Pace University Pace Plaza, New York 10038, NY, USALet 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.http://dx.doi.org/10.1155/S0161171298000039NormalLindelöfcountable compact lattices; strongly σ-smooth measures. |
| spellingShingle | Carmen Vlad On lattice-topological properties of general Wallman spaces International Journal of Mathematics and Mathematical Sciences Normal Lindelöf countable compact lattices; strongly σ-smooth measures. |
| title | On lattice-topological properties of general Wallman spaces |
| title_full | On lattice-topological properties of general Wallman spaces |
| title_fullStr | On lattice-topological properties of general Wallman spaces |
| title_full_unstemmed | On lattice-topological properties of general Wallman spaces |
| title_short | On lattice-topological properties of general Wallman spaces |
| title_sort | on lattice topological properties of general wallman spaces |
| topic | Normal Lindelöf countable compact lattices; strongly σ-smooth measures. |
| url | http://dx.doi.org/10.1155/S0161171298000039 |
| work_keys_str_mv | AT carmenvlad onlatticetopologicalpropertiesofgeneralwallmanspaces |