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A triple of infinite iterates of the functor of positively homogeneous functionals
G. F. Djabbarov Nizami Tashkent State Pedagogical University, Tashkent, Uzbekistan
Abstract:
The present article is devoted to the study of the space OH(X) of all weakly additive order-preserving normalized positively homogeneous functionals on a metric compactum X. We prove the uniform metrizability of the functor OH by means of the Kantorovich–Rubinshteĭn metric. We also show that the functor OH+ is perfectly metrizable, where OH+(X)={μ∈OH(X):|μ(φ)|⩽μ(|φ|),φ∈C(X)}. Under natural assumptions on X, we show that the triple (Fω(X),F++(X),F+(X)) is homeomorphic to (Q,s,rintQ), where F is a convex seminormal semimonadic subfunctor of OH+.
Key words:
weakly additive functional, Kantorovich–Rubinshteĭn metric, seminormal functor, perfectly metrizable functor, convex functor.
Received: 02.03.2018 Revised: 25.04.2018 Accepted: 23.05.2018
Citation:
G. F. Djabbarov, “A triple of infinite iterates of the functor of positively homogeneous functionals”, Mat. Tr., 22:1 (2019), 101–118; Siberian Adv. Math., 29:3 (2019), 190–201
Linking options:
https://www.mathnet.ru/eng/mt349 https://www.mathnet.ru/eng/mt/v22/i1/p101
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Abstract page: | 282 | Full-text PDF : | 57 | References: | 57 | First page: | 10 |
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