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Removing critical pairs

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Abstract

A long-standing conjecture in dimension theory asserts that every ordered set with at least three elements contains two elements whose removal decreases the dimension by at most one. We disprove the yet stronger conjecture that the removal of any critical pair decreases the dimension by at most one. We have constructed the counterexample using Ferrers dimension which will be described in this paper.

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Authors and Affiliations

  1. Technische Hochschule Darmstadt, D-6100, Darmstadt, West Germany

    Klaus Reuter

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  1. Klaus Reuter
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Communicated by I. Rival

AMS subject classification (1980). 06A10.

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Reuter, K. Removing critical pairs. Order 6, 107–118 (1989). https://doi.org/10.1007/BF02034329

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  • DOI: https://doi.org/10.1007/BF02034329

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