A short proof that \(N^ 3\) is not a circle containment order (Q1115459)
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scientific article; zbMATH DE number 4085717
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A short proof that \(N^ 3\) is not a circle containment order |
scientific article; zbMATH DE number 4085717 |
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A short proof that \(N^ 3\) is not a circle containment order (English)
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1988
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A partially ordered set P is called a circle containment order if there is a correspondence \(x\to C_ x\) from P into circles in the plane such that \(x\leq y\Leftrightarrow C_ x\subseteq C_ y\). The author shows that the infinite three-dimensional poset \(N^ 3\) is not a circle containment order and notes that it is still unknown whether or not \([n]^ 3\) is such an order for arbitrarily large n.
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circle containment order
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infinite three-dimensional poset \(N^ 3\)
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