Topological Aspects of the Product of Lattices
Let 𝐗 be an arbitrary nonempty set and 𝐋 a lattice of subsets of 𝐗 such that ∅, X∈L. 𝐀(𝐋) denotes the algebra generated by 𝐋, and 𝐌(𝐋) denotes those nonnegative, finite, finitely additive measures on 𝐀(𝐋). In addition, 𝐈(𝐋) denotes the subset of 𝐌(𝐋) which consists of the nontrivial zero-one valued...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/920737 |
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| author | Carmen Vlad |
| author_facet | Carmen Vlad |
| author_sort | Carmen Vlad |
| collection | DOAJ |
| description | Let 𝐗 be an arbitrary nonempty set and 𝐋 a lattice of subsets of 𝐗 such that ∅, X∈L. 𝐀(𝐋) denotes the algebra generated by 𝐋, and 𝐌(𝐋) denotes those nonnegative, finite, finitely additive measures on 𝐀(𝐋). In addition, 𝐈(𝐋) denotes the subset of 𝐌(𝐋) which consists of the nontrivial zero-one valued measures. The paper gives detailed analysis of products of lattices, their associated Wallman spaces, and products of a variety of measures. |
| format | Article |
| id | doaj-art-acfd93a2068b423daa8f03255dcb5ea3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-acfd93a2068b423daa8f03255dcb5ea32025-02-03T01:22:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/920737920737Topological Aspects of the Product of LatticesCarmen Vlad0Department of Mathematics, Pace University, Pleasantville, NY 10570, USALet 𝐗 be an arbitrary nonempty set and 𝐋 a lattice of subsets of 𝐗 such that ∅, X∈L. 𝐀(𝐋) denotes the algebra generated by 𝐋, and 𝐌(𝐋) denotes those nonnegative, finite, finitely additive measures on 𝐀(𝐋). In addition, 𝐈(𝐋) denotes the subset of 𝐌(𝐋) which consists of the nontrivial zero-one valued measures. The paper gives detailed analysis of products of lattices, their associated Wallman spaces, and products of a variety of measures.http://dx.doi.org/10.1155/2011/920737 |
| spellingShingle | Carmen Vlad Topological Aspects of the Product of Lattices International Journal of Mathematics and Mathematical Sciences |
| title | Topological Aspects of the Product of Lattices |
| title_full | Topological Aspects of the Product of Lattices |
| title_fullStr | Topological Aspects of the Product of Lattices |
| title_full_unstemmed | Topological Aspects of the Product of Lattices |
| title_short | Topological Aspects of the Product of Lattices |
| title_sort | topological aspects of the product of lattices |
| url | http://dx.doi.org/10.1155/2011/920737 |
| work_keys_str_mv | AT carmenvlad topologicalaspectsoftheproductoflattices |