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Valentine convexity in n dimensions
Published online by Cambridge University Press: 24 October 2008
Extract
A subset X of Euclidean space such that if a, b, c are points of X then at least one of the segments joining two of them lies in X, is said to be V-convex. Valentine (4) showed that in two dimensions a compact V-convex set is the union of at most three convex sets. We show here that if the set of star centres of X is of lower dimension than X and X is a compact V-convex set then it is the union of at most two convex sets.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 2 , September 1976 , pp. 223 - 228
- Copyright
- Copyright © Cambridge Philosophical Society 1976