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Valentine convexity in n dimensions

Published online by Cambridge University Press:  24 October 2008

H. G. Eggleston
H. G. Eggleston
Affiliation:
Royal Holloway College, University of London
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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

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References

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