Article ID Journal Published Year Pages File Type
5778000 Topology and its Applications 2017 11 Pages PDF
Abstract
The present paper is devoted to study of the space of all weakly additive, order-preserving, normalized and positively-homogeneous functionals on a metric compactum. We construct an analogue of a modified Kantorovich-Rubinstein metric on the space OH(X) of all weakly additive, order-preserving, normalized and positively-homogeneous functionals on a metric compactum X. We prove that the functor OH is metrizable. We also show that for any metric compactum X the hyperspace exp(X) equipped with the Hausdorff metric can be isometrically embedded into OH(X).
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Physical Sciences and Engineering Mathematics Geometry and Topology
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