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The authors consider the class C of closed convex cones in a Hilbert space as a topological space and investigate the resulting topological properties of certain mappings into C. They show that with the proper choice of a Hausdorff metric for C the operation of taking the polar cone is an involutory isometry. The operation is considered of taking the positive hull of a finite set of points as a mapping into C and obtain some sufficient conditions for the continuity of this mapping. (Author)
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Walkup et al. (1967) studied this question.
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