Geodesic
The Lattice of all Topologies is Complemented
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 805-807

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

In (3), J. Hartmanis raised the question whether the lattice of all topologies in a given set is complemented and gave the affirmative answer for the case of a finite set. H. Gaifman (2), has extended this result to denumerable sets. Using Gaifman's paper, Anne K. Steiner (4) has proved that the lattice is always complemented. Our aim in this article is to give an alternative proof, independent of Gaifman's results. So far, Steiner's proof has not been available to the author. 
Rooij, A. C. M. Van. The Lattice of all Topologies is Complemented. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 805-807. doi: 10.4153/CJM-1968-079-9
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[1] 1. Birkhoff, G., Lattice theory, Amer. Math. Soc. Colloq. Publ., Vol. 25 (Amer. Math. Soc, Providence, R.I., 1960). Google Scholar

[2] 2. Gaifman, H., The lattice of all topologies, Can. J. Math. 18 (1966), 83–88. Google Scholar

[3] 3. Hartmanis, J., On the lattice of topologies, Can. J. Math. 10 (1958), 547–553. Google Scholar

[4] 4. Steiner, Anne K., The topological complementation problem, Technical report No. 84, 1965, Univ. of New Mexico. Google Scholar

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