An n + 1 Member Decomposition for Sets Whose Lnc Points Form n Convex Sets
Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1378-1383

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Let S be a subset of Rd. A point x in 5 is a point of local convexity of S if and only if there is some neighborhood N of x such that, if y, z ∈ N ᑎ 5, then [y, z] ⊆ S. If S fails to be locally convex at some point q in S then q is called a point of local nonconvexity (lnc point) of S.
Breen, Marilyn. An n + 1 Member Decomposition for Sets Whose Lnc Points Form n Convex Sets. Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1378-1383. doi: 10.4153/CJM-1975-140-2
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[1] 1. Breen, Marilyn, Points of local nonconvexity and finite unions of convex sets, Can. J. Math. 27 (1975), 376–383. Google Scholar

[2] 2. Guay, Merle D. and Kay, David C., On sets having finitely many points of local nonconvexity and property Pm, Israel J. Math. 10 (1971), 196–209. Google Scholar

[3] 3. Lawrence, J. F., Hare, W. R., and Kenelly, John W., Finite unions of convex sets, Proc. Amer. Math. Soc. 34 (1972), 225–228. Google Scholar

[4] 4. Valentine, F. A., Convex sets (McGraw-Hill, New York, 1964). Google Scholar

[5] 5. Valentine, F. A., Local convexity and Ln sets, Proc. Amer. Math. Soc. 16 (1965), 1305–1310. Google Scholar

[6] 6. Valentine, F. A., A three p0ini convexity property, Pacific J. Math. 7 (1957), 1227–1235. Google Scholar

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