Abstract
Using the ideas of Scheinerman and Wierman [1] and of Hurlbert [2] we give a very short proof that the infinite order [2]×[3]×ω cannot be represented by containment of Euclidean balls in ad-dimensional space for anyd. Also we give representations of the orders [2]×[2]×ω and [3]×[3]×[3] by containment of circles in the plane.
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References
E. R. Scheinerman and J. C. Wierman (1988) On circle containment orders,Order 4, 315–318.
G. Hurlbert (1988) A short proof thatN 3 is not a circle containment order,Order 5, 235–237.
G. Brightwell and P. Winkler (1989) Sphere orders,Order 6, 235–240.
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Communicated by I. Rival
The work was financially supported by the Russian Foundation of Fundamental Research, Grant 93-011-1486
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Fon-Der-Flaass, D.G. A note on sphere containment orders. Order 10, 143–145 (1993). https://doi.org/10.1007/BF01111298
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DOI: https://doi.org/10.1007/BF01111298