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On the Lattice of σ-Algebras

Published online by Cambridge University Press:  20 November 2018

Marlon C. Rayburn
Marlon C. Rayburn*
Affiliation:
State University of New York at Geneseo, Geneseo, New York; The University of Kentucky, Lexington, Kentucky
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 755 - 761
Copyright
Copyright © Canadian Mathematical Society 1969

References

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