Strictly ergodic, uniform positive entropy models
Striped structures of stable and unstable sets of expansive homeomorphisms and a theorem of K. Kuratowski on independent sets
We investigate striped structures of stable and unstable sets of expansive homeomorphisms and continuum-wise expansive homeomorphisms. The following theorem is proved: if f : X → X is an expansive homeomorphism of a compact metric space X with dim X > 0, then the decompositions and of X into stable and unstable sets of f respectively are uncountable, and moreover there is σ (= s or u) and ϱ > 0 such that there is a Cantor set C in X with the property that for each x ∈ C, contains a nondegenerate...
Strong convergence and control condition of modified Halpern iterations in Banach spaces.
Strong convergence for accretive operators in Banach spaces.
Strong convergence of a modified implicit iteration process for a finite family of -operators.
Strong convergence of an implicit algorithm in CAT(0) spaces.
Strong convergence of an iterative method for equilibrium problems and variational inequality problems.
Strong convergence of approximation fixed points for nonexpansive nonself-mapping.
Strong convergence of modified Halpern iterations in spaces.
Strong convergence theorems for equilibrium problems and quasi-- asymptotically nonexpansive mappings in Banach spaces.
Structure of certain closed flows
Structure of dynamical systems
Subcontinua of inverse limit spaces of unimodal maps
We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal maps as...
Subgroups and products of -factorizable -groups
We show that every subgroup of an -factorizable abelian -group is topologically isomorphic to a closed subgroup of another -factorizable abelian -group. This implies that closed subgroups of -factorizable -groups are not necessarily -factorizable. We also prove that if a Hausdorff space of countable pseudocharacter is a continuous image of a product of -spaces and the space is pseudo--compact, then . In particular, direct products of -factorizable -groups are -factorizable and...
Subgroups of -factorizable groups.
Subgroups of -factorizable groups
The properties of -factorizable groups and their subgroups are studied. We show that a locally compact group is -factorizable if and only if is -compact. It is proved that a subgroup of an -factorizable group is -factorizable if and only if is -embedded in . Therefore, a subgroup of an -factorizable group need not be -factorizable, and we present a method for constructing non--factorizable dense subgroups of a special class of -factorizable groups. Finally, we construct a closed...
Subsequential limits of fixed point sets
Subshifts of Finite Type and Sofic Systems.
Suites à termes dans un alphabet fini
Summable Family in a Commutative Group
Hölzl et al. showed that it was possible to build “a generic theory of limits based on filters” in Isabelle/HOL [22], [7]. In this paper we present our formalization of this theory in Mizar [6]. First, we compare the notions of the limit of a family indexed by a directed set, or a sequence, in a metric space [30], a real normed linear space [29] and a linear topological space [14] with the concept of the limit of an image filter [16]. Then, following Bourbaki [9], [10] (TG.III, §5.1 Familles sommables...