The lattice of ideals of a compact semilattice

Stralka, A. R.

doi:10.1090/S0002-9939-1972-0308325-8

The lattice of ideals of a compact semilattice
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by A. R. Stralka PDF

Proc. Amer. Math. Soc. 33 (1972), 175-180 Request permission

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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