All finite distributive lattices occur as intervals between Hausdorff topologies (Q1267549)
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scientific article; zbMATH DE number 1210055
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | All finite distributive lattices occur as intervals between Hausdorff topologies |
scientific article; zbMATH DE number 1210055 |
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All finite distributive lattices occur as intervals between Hausdorff topologies (English)
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30 May 1999
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The authors show that a finite lattice is isomorphic to an interval between two \(T_2\)-topologies if and only if it is distributive. This result has been obtained earlier by C. Good, W. S. Watson and the third author in ZFC under the assumption of the existence of infinitely many measurable cardinals. The presented proof needs no such assumption.
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finite distributive lattices
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intervals between Hausdorff topologies
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lattice of topologies
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