Which distributive lattices are lattices of closed sets?
1959 ◽
Vol 55
(2)
◽
pp. 172-176
◽
Keyword(s):
1. An elegant theorem due to Tarski states that a completely distributive complete Boolean algebra is isomorphic with a lattice of sets, and in fact the lattice of all the subsets of some aggregate. The obvious generalization of the question underlying this theorem is to ask whether one can pick out by means of a distributivity condition those lattices (not necessarily Boolean algebras) which are isomorphs of lattices of sets. The answer is no. The real numbers with their natural order form a complete lattice which satisfies the strongest possible distributivity conditions and yet is not iso-morphic with any lattice of sets.
Keyword(s):
1979 ◽
Vol 27
(2)
◽
pp. 248-256
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Keyword(s):
1978 ◽
Vol 68
(2)
◽
pp. 217-217
1979 ◽
Vol 73
(3)
◽
pp. 405
Keyword(s):
Keyword(s):