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.
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 52A20
Retrieve articles in all journals with MSC: 52A20
Keywords: Convex, locally convex, local nonconvexity, set, Tietze's theorem
Article copyright: © Copyright 1979 American Mathematical Society