Iterative processes and open mapping theorems
James boundaries and σ-fragmented selectors
We study the boundary structure for w*-compact subsets of dual Banach spaces. To be more precise, for a Banach space X, 0 < ϵ < 1 and a subset T of the dual space X* such that ⋃ B(t,ϵ): t ∈ T contains a James boundary for we study different kinds of conditions on T, besides T being countable, which ensure that . (SP) We analyze two different non-separable cases where the equality (SP) holds: (a) if is the duality mapping and there exists a σ-fragmented map f: X → X* such that B(f(x),ϵ)...
Joint continuity of function spaces
Joint continuity of sequentially continuous maps
Jumps of entropy in one dimension
-systems, -networks and -covers
The concepts of -systems, -networks and -covers were defined by A. Arhangel’skiǐ in 1964, P. O’Meara in 1971 and R. McCoy, I. Ntantu in 1985, respectively. In this paper the relationships among -systems, -networks and -covers are further discussed and are established by -systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given by means of -systems.
does not imply .
Kac’s chaos and Kac’s program
In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in [33] which gives a possible answer to some questions formulated by Kac in [25]. We also present some related recent results about Kac’s chaos and Kac’s program obtained in [34, 23, 13] by K. Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.
Kadec Norms on Spaces of Continuous Functions
2000 Mathematics Subject Classification: Primary: 46B03, 46B26. Secondary: 46E15, 54C35.We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing the class of compact...
Katetov Extension as a Functor.
KKM theorem with applications to lower and upper bounds equilibrium problem in -convex spaces.
Kneading sequences of skew tent maps
Kovergenz in Verallgemeinerten Topologischen Räumen
Krasinkiewicz maps from compacta to polyhedra
We prove that the set of all Krasinkiewicz maps from a compact metric space to a polyhedron (or a 1-dimensional locally connected continuum, or an n-dimensional Menger manifold, n ≥ 1) is a dense -subset of the space of all maps. We also investigate the existence of surjective Krasinkiewicz maps from continua to polyhedra.
K-space function spaces.
Kuratowski convergence on compacta and Hausdorff metric convergence on compacta
This paper completes and improves results of [10]. Let , be two metric spaces and be the space of all -valued continuous functions whose domain is a closed subset of . If is a locally compact metric space, then the Kuratowski convergence and the Kuratowski convergence on compacta coincide on . Thus if and are boundedly compact metric spaces we have the equivalence of the convergence in the Attouch-Wets topology (generated by the box metric of and ) and convergence on ,...
-Непрерывные селекторы неподвижных точек многозначных отображений с разложимыми значениями. III. Приложения
-непрерывные селекторы неподвижных точек многозначных отображений с разложимыми значениями. I: Теоремы существования.
-Непрерывные селекторы неподвижных точек многозначных отображений с разложимыми значениями. II. Теоремы релаксации
-Ponomarev’s System and Images of Locally Separable Metric Spaces