|ISSN 1088-6826(online) ISSN 0002-9939(print)|
A counterexample to a ``theorem'' on sets
Abstract: An example is given of a closed connected set in whose points of local nonconvexity can be decomposed into two convex subsets, but which is not arcwise connected and hence is not an set. This contradicts a result by Valentine to which Stavrakas and Jamison have given a second proof. It is also shown that if the set of points of local nonconvexity of a closed connected set S in can be decomposed into n compact subsets which are convex relative to S, then S is an set.
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