Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Two cells with $ n$ points of local nonconvexivity

Authors: Nick M. Stavrakas, W. R. Hare and J. W. Kenelly
Journal: Proc. Amer. Math. Soc. 27 (1971), 331-336
MSC: Primary 52.30
MathSciNet review: 0270273
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Abstract: A subset $ S$ of the plane is a two cell provided $ S$ is homeomorphic to $ \{ x\vert\;\vert\vert x\vert\vert \leqq 1\} $.

Theorem. Let $ S$ be a two cell with exactly $ n$ points of local nonconvexity. Then $ S$ is expressible as a union of $ n + 1$ compact convex sets with mutually disjoint interiors.

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Keywords: Convex set, local convexity, two cell
Article copyright: © Copyright 1971 American Mathematical Society