Families of mutually complementary topologies

Anderson, B. A.

doi:10.1090/S0002-9939-1971-0281141-0

Families of mutually complementary topologies
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by B. A. Anderson

Proc. Amer. Math. Soc. 29 (1971), 362-368

DOI: https://doi.org/10.1090/S0002-9939-1971-0281141-0

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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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A sublattice of the lattice of topologies

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