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On the Lattice of Topologies

Published online by Cambridge University Press:  20 November 2018

Juris Hartmanis
Juris Hartmanis*
Affiliation:
Ohio State University
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In many cases Lattice Theory has proven itself to be useful in the study of the totality of mathematical systems of a given type. In this paper we shall continue one of such studies by investigating further the lattice of all topologies on a given set S. A considerable amount of research has been done in this field (1; 2; 3; 5; 6). This research, besides satisfying the intrinsic interest in the lattice theoretic properties of this lattice, has aided the study of interconnections of different properties of point set topologies.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 547 - 553
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Bagley, R. W., On the characterization of the lattice of topologies, J. Lond. Math. Soc, 30 (1955), 247-249.Google Scholar
2. Bagley, R. W. and Ellis, David, On the topolattice and permutation group of an infinite set, Math. Japon., 3 (1954), 63-70.Google Scholar
3. Birkhoff, G., On the combination of topologies, Fund. Math., 26 (1936), 156-166.Google Scholar
4. Hartmanis, Juris, Two embedding theorems for finite lattices, Proc. Amer. Math. Soc, 7 (1956), 571–577.Google Scholar
5. Hewitt, Edwin, A problem of set-theoretic topology, Duke Math. J., 10 (1943), 309-333.Google Scholar
6. Vaidyanathaswami, R., Treatise on set topology, Indian Math. Soc. (Madras, 1947).Google Scholar