A proof of a theorem of Valentine
Published online by Cambridge University Press: 24 October 2008
Extract
An interesting extension of the idea of convexity has been introduced by Valentine (2). He considered a plane set X such that for any three points a, b, c in X at least one of the segments [a, b], [b, c], [c, a] is contained in X, and showed that such a set can be regarded as the union of at most three convex sets. See also (3). The five pointed star (Fig. 1) is an example that shows that X may not be the union of fewer than three convex sets.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 3 , May 1975 , pp. 525 - 528
- Copyright
- Copyright © Cambridge Philosophical Society 1975
References
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