Hostname: page-component-7dd5485656-kp629 Total loading time: 0 Render date: 2025-10-31T00:58:55.412Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Lattice of Topologies

Published online by Cambridge University Press:  20 November 2018

Juris Hartmanis
Juris Hartmanis*
Affiliation:
Ohio State University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Information

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