Elementary properties of arcwise connected sets and functions
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The purpose of this paper is to investigate some elementary, basic properties of arcwise connected sets and functions. Since these concepts are generalizations of convexity, it is natural to ask if any of the basic properties of convex sets and functions are carried over to these new generalized classes. All the functions involved are considered to be not necessarily differentiable.
Key WordsConvexity arcwise connectedness continuity locally bounded functions Lipschitz condition epigraph
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