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Proceedings of the American Mathematical Society

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Codimension of compact $ M$-semilattices


Authors: J. W. Lea and A. Y. W. Lau
Journal: Proc. Amer. Math. Soc. 52 (1975), 406-408
MSC: Primary 22A99
DOI: https://doi.org/10.1090/S0002-9939-1975-0374324-6
MathSciNet review: 0374324
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Abstract: This paper is a generalization of [5] and gives a partial answer to Question 31 in [1], i.e., if $ S$ is a compact $ M$-semilattice of finite codimension and $ x \ne y$, then there exists a closed subsemilattice $ A$ of $ S$ such that $ A$ separates $ x$ and $ y$ in $ S$ and $ \operatorname{cd} A < \operatorname{cd} S$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0374324-6
Article copyright: © Copyright 1975 American Mathematical Society