Geodesic
On the Lattice of σ-Algebras
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 755-761

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Rayburn, Marlon C. On the Lattice of σ-Algebras. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 755-761. doi: 10.4153/CJM-1969-086-9
@article{10_4153_CJM_1969_086_9,
     author = {Rayburn, Marlon C.},
     title = {On the {Lattice} of {\ensuremath{\sigma}-Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {755--761},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-086-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-086-9/}
}
TY  - JOUR
AU  - Rayburn, Marlon C.
TI  - On the Lattice of σ-Algebras
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 755
EP  - 761
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-086-9/
DO  - 10.4153/CJM-1969-086-9
ID  - 10_4153_CJM_1969_086_9
ER  - 
%0 Journal Article
%A Rayburn, Marlon C.
%T On the Lattice of σ-Algebras
%J Canadian journal of mathematics
%D 1969
%P 755-761
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-086-9/
%R 10.4153/CJM-1969-086-9
%F 10_4153_CJM_1969_086_9

[1] 1. Frôhlich, O., Das Halbordnungssystern der topologischen Râume auf einer Menge, Math. Ann. 156 (1964), 79–95. Google Scholar

[2] 2. Kelley, P. J., General topology (Van Nostrand, New York, 1955). Google Scholar

[3] 3. Krishnamurthy, V., On the number of topologies on a finite set, Amer. Math. Monthly 73 (1966), 154–157. Google Scholar

[4] 4. Munroe, M. E., Introduction to measure and integration (Addison-Wesley, Reading, Mass., 1953). Google Scholar

[5] 5. Rayburn, M., On the Borel fields of a finite set, Proc. Amer. Math. Soc. 19 (1968), 885–889. Google Scholar

[6] 6. Sharp, H., Homeomorphisms on finite sets, Math. Mag. 40 (1967), 152–155. Google Scholar

[7] 7. Steiner, A. K., The lattice of topologies: structure and complementation, Trans. Amer. Math. Soc. 121 (1966), 379–398. Google Scholar

Cité par Sources :