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The lattice of ideals of a compact semilattice


Author: A. R. Stralka
Journal: Proc. Amer. Math. Soc. 33 (1972), 175-180
MSC: Primary 22A30; Secondary 06A20, 54H10
DOI: https://doi.org/10.1090/S0002-9939-1972-0308325-8
MathSciNet review: 0308325
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Abstract: It is shown that, if L is a compact distributive topological lattice with enough continuous join-preserving maps into I to separate points, then there is a continuous lattice homomorphism from $ \mathcal{M}(L)$, the lattice of M-closed subsets of L, onto L. If $ J(L)$, the set of join-irreducible elements of L, is a compact semilattice then L is iseomorphic with $ \mathcal{M}(J(L))$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0308325-8
Keywords: Compact semilattice, lattice of ideals
Article copyright: © Copyright 1972 American Mathematical Society

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