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Stone Space


Let P(L) be the set of all prime ideals of L, and define r(a)={P|a not in 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

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References

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

Referenced on Wolfram|Alpha

Stone Space

Cite this as:

Weisstein, Eric W. "Stone Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StoneSpace.html

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