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A short proof that N 3 is not a circle containment order
Authors:Hurlbert  Glenn H
Institution:(1) Department of Mathematics, SUNY, 11794 Stony Brook, NY, U.S.A.
Abstract:A partially ordered set P is called a circle containment order provided one can assign to each xisinP a circle C x so that 
$$x \leqslant y \Leftrightarrow C_x  \subseteq C_y $$
. We show that the infinite three-dimensional poset N 3 is not a circle containment order and note that it is still unknown whether or not n]3 is such an order for arbitrarily large n.
Keywords:06A10
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