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Sphere orders

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Abstract

Ann-sphere order is a finite partially ordered set representable by containment ofn-spheres in Euclidean (n+1)-space. We present a sequence {P i } of ordered sets such that eachP i is ann-sphere order only forn≥i; one consequence is that we are able to determine the dimension of a Euclidean space-time manifold from the finite suborders of its causality order.

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Authors and Affiliations

  1. London School of Economics and Political Science, Houghton St., WC2A 2AE, London, United Kingdom

    Graham Brightwell

  2. Bellcore, 445 South St., 07960-1910, Morristown, NJ, U.S.A.

    Peter Winkler

Authors
  1. Graham Brightwell
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  2. Peter Winkler
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Additional information

Communicated by I. Rival

Research supported by ONR grant N00014 85-K-0769.

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Brightwell, G., Winkler, P. Sphere orders. Order 6, 235–240 (1989). https://doi.org/10.1007/BF00563524

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  • DOI: https://doi.org/10.1007/BF00563524

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