A partial order generalization of Alexander's subbase theorem |
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Authors: | Alexander Abian |
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Institution: | 1. Department of Mathematics, Iowa State University, 50011, Ames, Iowa, USA
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Abstract: | 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. |
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Keywords: | 1980 Mathematics Subject Classification" target="_blank">1980 Mathematics Subject Classification Primary 06A99 |
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