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On the Lattice of σ-Algebras
Published online by Cambridge University Press: 20 November 2018
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In this paper I consider the relations between the lattice of topologies on a fixed space and the lattice of σ-algebras on that space. It is found that the intersection of these two lattices is the lattice of complete Boolean algebras, and that this lattice is anti-atomically generated. Some sufficient conditions for a topology to contain a maximal σ-algebra are noted.
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- Copyright © Canadian Mathematical Society 1969