All Finite Distributive Lattices Occur as Intervals Between Hausdorff Topologies |
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| Authors: | Knight R. W. Gartside P. Mcintyre D. W. |
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| Affiliation: | (1) Department of Mathematics, Oxford University, U.K.;(2) University of Auckland, Auckland, New Zealand |
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| Abstract: | It is shown that a finite lattice L is isomorphic to the interval betweentwo Hausdorff topologies on some set if and only if L is distributive. Thecorresponding results had previously been shown in ZFC for intervals between T1 topologies and, assuming the existence of infinitely manymeasurable cardinals, for intervals between T3 topologies. |
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| Keywords: | lattice of topologies |
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