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a-convexity

Published online by Cambridge University Press:  24 October 2008

R. G. E. Pinch
R. G. E. Pinch
Affiliation:
Department of Mathematics, University of Glasgow
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Extract

For a ε R, we define a subset V of Rn to be a-convex if x, y ε V implies

Clearly V is (1 — a)-convex iff it is a-convex: V is convex iff it is a-convex for all a ε [0, 1], and any set is 1-convex. We define the a-convex hull of V to be the intersection of all a-convex subsets of Rn containing V. Put D = 0,1} and D(a) the a-convex hull of D in R1. If V is a-convex and x, y ε V, then V must contain the points of the line through x, y given by {tx + (1 — t) y: t ε D(a)} and so in this paper we concentrate on the study of D(a).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 1 , January 1985 , pp. 63 - 68
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

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