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A Decomposition Theorem for m-Convex Sets in Rd

Published online by Cambridge University Press:  20 November 2018

Marilyn Breen
Marilyn Breen*
Affiliation:
University of Oklahoma, Norman, Oklahoma
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Let S be a subset of some linear topological space. The set S is said to be m-convex, m ≧ 2, if and only if for every m-member subset of S, at least one of the line segments determined by these points lies in S. A point x in S is said to be a point of local convexity of S if and only if there is some neighborhood N of x such that if y, z Є N ⌒ S, then [y, z] ⊆ S. If S fails to be locally convex at some point a in S, then q is called a point of local nonconvexity (lnc point) of S.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 1051 - 1057
Copyright
Copyright © Canadian Mathematical Society 1976

References

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