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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

1. Frôhlich, O., Das Halbordnungssystern der topologischen Râume auf einer Menge, Math. Ann. 156 (1964), 79–95.Google Scholar
2. Kelley, P. J., General topology (Van Nostrand, New York, 1955).Google Scholar
3. Krishnamurthy, V., On the number of topologies on a finite set, Amer. Math. Monthly 73 (1966), 154–157.Google Scholar
4. Munroe, M. E., Introduction to measure and integration (Addison-Wesley, Reading, Mass., 1953).Google Scholar
5. Rayburn, M., On the Borel fields of a finite set, Proc. Amer. Math. Soc. 19 (1968), 885–889.Google Scholar
6. Sharp, H., Homeomorphisms on finite sets, Math. Mag. 40 (1967), 152–155.Google Scholar
7. Steiner, A. K., The lattice of topologies: structure and complementation, Trans. Amer. Math. Soc. 121 (1966), 379–398.Google Scholar