Two cells with $n$ points of local nonconvexivity
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- by Nick M. Stavrakas, W. R. Hare and J. W. Kenelly PDF
- Proc. Amer. Math. Soc. 27 (1971), 331-336 Request permission
Abstract:
A subset $S$ of the plane is a two cell provided $S$ is homeomorphic to $\{ x|\;||x|| \leqq 1\}$. 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.References
- M. H. A. Newman, Elements of the topology of plane sets of points, Cambridge, at the University Press, 1951. 2nd ed. MR 0044820
- Heinrich Tietze, Über Konvexheit im kleinen und im großen und über gewisse den Punkten einer Menge zugeordnete Dimensionszahlen, Math. Z. 28 (1928), no. 1, 697–707 (German). MR 1544985, DOI 10.1007/BF01181191
- F. A. Valentine, Local convexity and $L_{n}$ sets, Proc. Amer. Math. Soc. 16 (1965), 1305–1310. MR 185510, DOI 10.1090/S0002-9939-1965-0185510-6
- Frederick A. Valentine, Convex sets, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Toronto-London, 1964. MR 0170264
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 331-336
- MSC: Primary 52.30
- DOI: https://doi.org/10.1090/S0002-9939-1971-0270273-9
- MathSciNet review: 0270273