Results 1 to 10 of about 979 (94)
Uniformizable and realcompact bornological universes [PDF]
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 +7 more sources
Caristi Type Coincidence Point Theorem in Topological Spaces
Journal of Applied Mathematics, 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.
Jiang Zhu, Lei Wei, Cheng-Cheng Zhu
doaj +2 more sources
Some remarks about Mackey convergence
International Journal of Mathematics and Mathematical Sciences, 1995 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
Józef Burzyk, Thomas E. Gilsdorf
doaj +2 more sources
International Journal of Mathematics and Mathematical Sciences, 1991 The purpose of this note is to extend Warner's idea of bornological structures to cover non-locally convex situations and to develop a framework unifying several variations on an ultrabornological theme (for example, ultrabornological spaces, o ...
V. Murali
doaj +2 more sources
Fast complete locally convex linear topological spaces
International Journal of Mathematics and Mathematical Sciences, 1986 This is a study of relationship between the concepts of Mackey, ultrabornological, bornological, barrelled, and infrabarrelled spaces and the concept of fast completeness. An example of a fast complete but not sequentially complete space is presented.
Carlos Bosch +2 more
doaj +2 more sources
Mathematische Zeitschrift, 1996 Semi-bornological spaces are defined to be locally convex spaces having the Mackey property and for which sequential continuity of linear functionals is equivalent to continuity. Weakly semi-bornological spaces are obtained by relaxing the Mackey requirement.
SCHAEFER, H.H., Beatty, T.A.
openaire +1 more source
Barrelled and Bornological Function Spaces
Journal of Mathematical Analysis and Applications, 2000 A subset \(K\) of a completely regular topological space \(Y\) is \(t\)-bounded if \(f(K)\) is a bounded subset of \(\mathbb{R}\) for every real continuous function \(f\) on \(Y\). Let \(X\) be a completely regular topological space. \(\nu X\) is the real-compactification of \(X\).
Dontchev, Julian +2 more
openaire +1 more source
The Alexandroff property and the preservation of strong uniform continuity
Applied General Topology, 2010 In this paper we extend the theory of strong uniform continuity and strong uniform convergence, developed in the setting of metric spaces in, to the uniform space setting, where again the notion of shields plays a key role.
Gerald Beer
doaj +1 more source
The spaces OM and OC are ultrabornological a new proof
International Journal of Mathematics and Mathematical Sciences, 1985 In [1] Laurent Schwartz introduced the spaces 𝒪M and 𝒪′C of multiplication and convolution operators on temperate distributions. Then in [2] Alexandre Grothendieck used tensor products to prove that both 𝒪M and 𝒪′C are bornological.
Jan Kucera
doaj +1 more source
Hausdorff Dimension in Convex Bornological Spaces
Journal of Mathematical Analysis and Applications, 2002 Soit \(Z\) une partie d'un espace localement convexe bornologique \(X\). Pour un disque borné \(D\) de \(X\) et le sous-espace vectoriel \(X_D\) engendre par \(D\), on désigne par \(d_D(Z)\) la limite de la dimension de \(Z\cap X_D\cap X_D\), pour tous les disques bornés \(D'\) de \(X\) , puis par \(\dim_H(Z)\) (dite dimension de Hausdorff de \(Z\)) la
Almeida, J., Barreira, L.
openaire +1 more source