Abstract
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.
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