A partial order generalization of Alexander's subbase theorem
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Alexander's Subbase Theorem is generalized for partially ordered sets. Our generalization is nontrivial inasmuch as Alexander's Theorem pertains to the partially ordered set (T, ∪) whereT is the set of all the open sets of a topological space and thus\((\overline T ,\underline C )\) is a complete partially ordered set which is also join infinite distributive, whereas here our generalization pertains to any partially ordered set with a maximum 1 and which satisfies the rather weak «distributivity» condition given by (1) below.
1980 Mathematics Subject ClassificationPrimary 06A99
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