The paper deal with the properties need to give a metric structure to the collection of bounded, closed, non-empty, convex sets of an Hilbert space H: To this aim a sequence of distances hn is defined (h0 =Hausdorff distance). In this context an extremal point of a convex set is characterized as the maximal element w.r.t a lexicographic ordering induced by a well ordered base.
Properties of convex sets with application to the differential theory of multivalued functions / G. Stefani; P. Zecca. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 2, n.5:(1978), pp. 583-595. [10.1016/0362-546X(78)90006-8]
Properties of convex sets with application to the differential theory of multivalued functions
STEFANI, GIANNA;ZECCA, PIETRO
1978
Abstract
The paper deal with the properties need to give a metric structure to the collection of bounded, closed, non-empty, convex sets of an Hilbert space H: To this aim a sequence of distances hn is defined (h0 =Hausdorff distance). In this context an extremal point of a convex set is characterized as the maximal element w.r.t a lexicographic ordering induced by a well ordered base.
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