On a relation between the nonconvexity of a set and the nonconvexity of its \(\epsilon\)-neighborhood
The authors present examples of sets whose nonconvexity functions substantially differ from the nonconvexity functions of arbitrarily small neighborhoods of these sets. Moreover, it is shown that, in uniformly convex Banach spaces, conditions of the type ``the function of nonconvexity is less than one'' are stable with respect to taking \(\varepsilon\)-neighborhoods of sets.
scientific article; zbMATH DE number 1927762