Александровские чтения-2016 | 22-26 мая 2016
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 Имя: Djabbarov Gayratbay FarxadovichНазвание: Triples of infinite iterates of convex subfunctors on functor of the positively homogeneous functionals Город, страна: Tashkent, Uzbekistan Организация: Tashkent State Pedagogical University named after Nizami Абстракт: 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 the 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 investigate under what conditions subfunctors of the functor $$OH$$ will be perfectly metrizable. We prove that under natural assumptions on $$X$$ the triple $$(\mathcal{F}^\omega_+(X), \mathcal{F}^{++}_+(X), \mathcal{F}^+_+(X))$$ is homeomorphic to the triple $$(Q,s, \textrm{rint}\, Q),$$ where $$\mathcal{F}$$ is a convex subfunctor of the functor $$OH_+.$$