Geodesic
A Representation Theorem for Relatively Complemented Distributive Lattices
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 756-758

Voir la notice de l'article provenant de la source Cambridge University Press

In this note, we are concerned with the following generalization of a wellknown theorem of M. H. Stone; see (2, 8.2).Theorem 1. Let L be a relatively complemented distributive lattice. (I) If L has no least element, then L is isomorphic to the lattice of non-empty compact-open subsets of an anti-Hausdorff, nearly-Hausdorff, T1-space with a base of open sets consisting of compact-open sets.(II) (3, Theorem 1) If L has a least element, then L is isomorphic to the lattice of all compact-open subsets of a locally compact totally disconnected space. Moreover, the spaces of (I) and (II) are compact if and only if L has a greatest element.The space in question is the space of prime ideals of L with the hull-kernel topology.The author is indebted to M. G. Stanley for several conversations concerning this note. 
Nanzetta, Philip. A Representation Theorem for Relatively Complemented Distributive Lattices. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 756-758. doi: 10.4153/CJM-1968-075-x
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[3] 3. Stone, M. H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc, 41 (1937), 375–481. Google Scholar

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