-completeness and fixpoint properties
-distributive function lattices
It is known that for a nonempty topological space and a nonsingleton complete lattice endowed with the Scott topology, the partially ordered set of all continuous functions from into is a continuous lattice if and only if both and the open set lattice are continuous lattices. This result extends to certain classes of -distributive lattices, where is a subset system replacing the system of all directed subsets (for which the -distributive complete lattices are just the continuous...
⊗-product of Markov matrices.
In this paper we introduce a ⊗-operation over Markov transition matrices, in the context of subshift of finite type, reproducing symbolic properties of the iterates of the critical point on a one-parameter family of unimodal maps. To the *-product between kneading sequences we associate a ⊗-product between the corresponding Markov matrices.
-approximation and fixed points of nonexpansive mappings in metric spaces
-энтропия выпуклых множеств и функций.
-discrete decomposability of completely additive families
-porosity is separably determined
We prove a separable reduction theorem for -porosity of Suslin sets. In particular, if is a Suslin subset in a Banach space , then each separable subspace of can be enlarged to a separable subspace such that is -porous in if and only if is -porous in . Such a result is proved for several types of -porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem...
-distance in a general topological space with application to fixed point theory.
ω-Limit sets for triangular mappings
In 1992 Agronsky and Ceder proved that any finite collection of non-degenerate Peano continua in the unit square is an ω-limit set for a continuous map. We improve this result by showing that it is valid, with natural restrictions, for the triangular maps (x,y) ↦ (f(x),g(x,y)) of the square. For example, we show that a non-trivial Peano continuum C ⊂ I² is an orbit-enclosing ω-limit set of a triangular map if and only if it has a projection property. If C is a finite union of Peano continua then,...
Аналитическая неразрешимость проблемы устойчивости и проблемы топологической классификации особых точек аналитических систем дифференциальных уравнений
Булевы -алгебры и квазиоткрытые отображения.
Вложения в топологические поля и построение поля, пространство которого не нормально
Внешние меры и внешние топологии
Воронки полунепрерывных полудинамических систем на плоскости
Геометрические свойства некоторых нелинейных динамических систем
Гладкие изоморфизмы, не имеющие квазиконформных дробных степеней
Гомотопический аналог теоремы Хелли и существование квазинеподвижных точек.
Групповые расширения минимальных множеств
Движения в полудинамических системах
Дзета-функции Райдемайстера, Нильсена и кручение Райдемайстера в теории динамических систем