Results 21 to 30 of about 181 (133)
Journal of Function Spaces, Volume 2016, Issue 1, 2016., 2016 We give necessary and sufficient conditions for exchange of limits of double‐indexed families, taking values in sets endowed with an abstract structure of convergence, and for preservation of continuity or semicontinuity of the limit family, with respect to filter convergence.
Antonio Boccuto +2 more
wiley +1 more source
Strong Proximal Continuity and Convergence
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 In several situations the notion of uniform continuity can be strengthened to strong uniform continuity to produce interesting properties, especially in constrained problems. The same happens in the setting of proximity spaces. While a parallel theory for uniform and strong uniform convergence was recently developed, and a notion of proximal ...
Agata Caserta +3 more
wiley +1 more source
Caristi Type Coincidence Point Theorem in Topological Spaces
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 A generalized Caristi type coincidence point theorem and its equivalences in the setting of topological spaces by using a kind of nonmetric type function are obtained. These results are used to establish variational principle and its equivalences in d‐complete spaces, bornological vector space, seven kinds of completed quasi‐semimetric spaces equipped ...
Jiang Zhu +3 more
wiley +1 more source
Statistical Convergence in Function Spaces
Abstract and Applied Analysis, Volume 2011, Issue 1, 2011., 2011 We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.
Agata Caserta +3 more
wiley +1 more source
An Ascoli theorem for sequential spaces
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 5, Page 303-315, 2001., 2001 Ascoli theorems characterize “precompact” subsets of the set of morphisms between two objects of a category in terms of “equicontinuity” and “pointwise precompactness,” with appropriate definitions of precompactness and equicontinuity in the studied category.
Gert Sonck
wiley +1 more source
Strictly barrelled disks in inductive limits of quasi‐(LB)‐spaces
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 727-732, 1996., 1996 A strictly barrelled disk B in a Hausdorff locally convex space E is a disk such that the linear span of B with the topology of the Minkowski functional of B is a strictly barrelled space. Valdivia′s closed graph theorems are used to show that closed strictly barrelled disk in a quasi‐(LB)‐space is bounded. It is shown that a locally strictly barrelled
Carlos Bosch, Thomas E. Gilsdorf
wiley +1 more source
Some remarks about Mackey convergence
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 4, Page 659-664, 1995., 1994 In this paper, we examine Mackey convergence with respect to K‐convergence and bornological (Hausdorff locally convex) spaces. In particular, we prove that: Mackey convergence and local completeness imply property K; there are spaces having K‐ convergent sequences that are not Mackey convergent; there exists a space satisfying the Mackey convergence ...
Józef Burzyk, Thomas E. Gilsdorf
wiley +1 more source
Ukrainian Mathematical Bulletin, 2019 A bornology $\mathcal{B}$ on a set $X$ is called minmax, if the smallest and largest coarse structures on $X$ compatible with $\mathcal{B}$ coincide. We prove that $\mathcal{B}$ is minmax, if and only if the family $\mathcal B^\sharp=\{p\in\beta X:\{X\setminus B:B\in\mathcal B\}\subset p\}$ consists of ultrafilters which are pairwise non ...
Banakh, Taras, Protasov, Igor
openaire +3 more sources
Uniformizable and realcompact bornological universes
Applied General Topology, 2009 Bornological universes were introduced some time ago by Hu and obtained renewed interest in recent articles on convergence in hyperspaces and function spaces and optimization theory.
Tom Vroegrijk
doaj +1 more source
Multivalued Usco Functions and Stegall Spaces
Revista de Ciencias, 2018 In this article we consider the study of the -differentiability and -ifferentiability for convex functions, not only in the general context of topological vector spaces (), but also in the context of Banach spaces.
Diana Ximena Narváez
doaj +1 more source