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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Families of mutually complementary topologies


Author: B. A. Anderson
Journal: Proc. Amer. Math. Soc. 29 (1971), 362-368
MSC: Primary 54.20
DOI: https://doi.org/10.1090/S0002-9939-1971-0281141-0
MathSciNet review: 0281141
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Abstract: Several lattices of topologies on an infinite set are considered and bounds are given for the sup of the set of cardinals d such that there is a family of d mutually complementary topologies. Large classes of $ {\aleph _0}$-topologies are shown to have $ {\aleph _0}$-complements, and an example is given to prove that complementation is not, in general, a very selective topological operation.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0281141-0
Keywords: Topologies, principal topologies, $ {T_1}$ topologies, $ {\aleph _0}$-topologies, lattice complementation
Article copyright: © Copyright 1971 American Mathematical Society