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Stone Space

Let $P(L)$ be the set of all Prime Ideals of $L$, and define $r(a)=\{P\vert a\notin P\}$. Then the Stone space of $L$ is the Topological Space defined on $P(L)$ by postulating that the sets of the form $r(a)$ are a subbase for the open sets.

See also Prime Ideal, Topological Space


Grätzer, G. Lattice Theory: First Concepts and Distributive Lattices. San Francisco, CA: W. H. Freeman, p. 119, 1971.

© 1996-9 Eric W. Weisstein