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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Hindawi Limited
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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |