The present chapter deals with some fundamental notions and facts on convex sets. It serves a double purpose: we establish certain properties of convex sets which shall be used later in the special case of convex polytopes; certain other properties are investigated which do not hold for all convex sets but are valid (and important) for more restricted families such as compact convex sets, polyhedral sets, or polytopes. We discuss these properties in order to enable the reader to place the convex polytopes in a better perspective among all convex sets.
KeywordsConvex Subset Convex Body Convex Cone Convex POLYTOPES Supporting Hyperplane
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