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The topological complementation theorem à la Zorn


Author: Paul S. Schnare
Journal: Proc. Amer. Math. Soc. 35 (1972), 285-286
MSC: Primary 54A05; Secondary 06A20
DOI: https://doi.org/10.1090/S0002-9939-1972-0296884-3
Erratum: Proc. Amer. Math. Soc. 65 (1977), 188.
MathSciNet review: 0296884
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Abstract: Steiner's topological complementation theorem is given a short simple proof using Zorn's Lemma.


References [Enhancements On Off] (What's this?)

  • [1] A. C. M. van Rooij, The lattice of all topologies is complemented, Canad. J. Math. 20 (1968), 805-807. MR 37 #3504. MR 0227920 (37:3504)
  • [2] P. S. Schnare, Infinite complementation in the lattice of topologies, Fund. Math. 64 (1969), 249-255. MR 39 #3444. MR 0242110 (39:3444)
  • [3] A. K. Steiner, The lattice of topologies: Structure and complementation, Trans. Amer. Math. Soc. 122 (1966), 379-398. MR 32 #8303. MR 0190893 (32:8303)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0296884-3
Keywords: Topological complementation theorem, lattice of topologies, principal topologies, complemented lattice
Article copyright: © Copyright 1972 American Mathematical Society

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