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Topological Aspects of the Product of Lattices

International Journal of Mathematics and Mathematical Sciences
Publication Date
  • Mathematics


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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