Results 31 to 40 of about 246 (128)

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

Well-posedness, bornologies, and the structure of metric spaces

Applied General Topology, 2009
Given a continuous nonnegative functional λ that makes sense defined on an arbitrary metric space (X, d), one may consider those spaces in which each sequence (xn) for which lim n→∞λ(xn) = 0 clusters. The compact metric spaces, the complete metric spaces,
Gerald Beer, Manuel Segura
doaj   +1 more source

On bornological induced pseudonearness [PDF]

, 2020
Pseudonearness is considered a common tool for studying bornology,b-topology, pseudoproximity, and last but not least,classicalnearness. For anypseudonear space we construct ab-completion, which generalizes the classical com-pletion of nearness spaces ...
Vaziry, Zohreh, Leseberg, Dieter
core   +1 more source

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

Total boundedness and bornologies [PDF]

, 2009
A set A in a metric space is called totally bounded if for each ε>0 the set can be ε-approximated by a finite set. If this can be done, the finite set can always be chosen inside A.
Beer, Gerald, Levi, Sandro
core   +1 more source

Extensions and Applications of Locally Solid Convergence Structures

Mathematics
Locally solid convergence structures provide a unifying framework for both topological and non-topological convergences in vector lattice theory. In this paper, we explore various extensions and applications of locally solid convergence structures.
Saeed Hashemi Sababe
doaj   +1 more source

Product metrics and boundedness

Applied General Topology, 2008
This paper looks at some possible ways of equipping a countable product of unbounded metric spaces with a metric that acknowledges the boundedness characteristics of the factors.
Gerald Beer
doaj   +1 more source

Boundary representations of locally compact hyperbolic groups

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract We develop the theory of Patterson–Sullivan measures for locally compact hyperbolic groups. This theory associates to certain left‐invariant metrics on the group measures on its boundary. Next, we establish irreducibility of the resulting (unitary) Koopman representations for second countable, nonelementary, unimodular locally compact ...
Michael Glasner
wiley   +1 more source