Compact Zero-Dimensional Metric Spaces of Finite Type
Jan 1972 · American Mathematical Society: Memoirs of the American Mathematical Society Book 130 · American Mathematical Soc.
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This monograph is devoted to the investigation of metric Boolean spaces that are of finite type. The first part contains uniqueness and existence theorems that reduce the study of the spaces under consideration to an investigation of the corresponding algebras [Fraktur capital]A(X). These algebras are characterized by identities, and they are referred to as topological Boolean algebras. In part two, the decompositions of a space X (of the kind under consideration) into disjoint unions and topological products are considered. These decompositions are related to corresponding algebraic decompositions of [Fraktur capital]A(X). Part three is devoted to the development of a duality theory for topological Boolean algebras.
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