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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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Keywords: Topologies, principal topologies, <IMG WIDTH="26" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${T_1}$"> topologies, <!– MATH ${\aleph _0}$ –> <IMG WIDTH="27" HEIGHT="39" ALIGN="MIDDLE" BORDER="0" SRC="images/img9.gif" ALT="${\aleph _0}$">-topologies, lattice complementation
Article copyright: © Copyright 1971 American Mathematical Society