Posets admitting a unique order-compatible topology |
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Authors: | David E. Dobbs |
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Affiliation: | Department of Mathematics, University of Tennessee, Knoxville, TN 37916, USA |
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Abstract: | A characterization is given for those posets (X, ?) such that X admits exactly one topology inducing the given partial order ?. As a corollary, a poset is finite if and only if it is finite-dimensional and admits a unique compatible topology. Related applications and examples are also developed. |
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