Bornological convergences

DOI10.1016/j.jmaa.2004.04.046zbMath1062.54012OpenAlexW4213131220MaRDI QIDQ1883372

Alojzy Lechicki, Sandro Levi, Andrzej Spakowski

Publication date: 12 October 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.04.046

zbMATH Keywords

convergencehyperspaceHausdorff metriccoveruniform structurebornologypretopologytotally bound set

Mathematics Subject Classification ID

Hyperspaces in general topology (54B20) Uniform structures and generalizations (54E15) Special constructions of topological spaces (spaces of ultrafilters, etc.) (54D80)

Related Items (29)

\(L\)-valued bornologies on powersets ⋮ Bornological modifications of hyperspace topologies ⋮ Gap topologies in metric spaces ⋮ Some properties of bornological convergences ⋮ Cardinal functions, bornologies and strong Whitney convergence ⋮ Uniform continuity, uniform convergence, and shields ⋮ Clopen linear subspaces and connectedness in function spaces ⋮ Bornological convergence and shields ⋮ The bornology of cofinally complete subsets ⋮ Structural properties of extended normed spaces ⋮ The structure of extended real-valued metric spaces ⋮ The weak Ekeland variational principle and fixed points ⋮ The Alexandroff one-point compactification as a prototype for extensions ⋮ Complete metrizability of topologies of strong uniform convergence on bornologies ⋮ On realcompactifications defined by bornologies ⋮ Strong Whitney and strong uniform convergences on a bornology ⋮ \(\mathcal S\)-topologies and bounded convergences ⋮ Bornological convergences on the hyperspace of a uniformizable space ⋮ On continuous convergence of nets of multifunctions ⋮ Bornological convergences and local proximity spaces ⋮ Convergence of partial maps ⋮ Cartesian closedness, extensionality and bornological universes ⋮ Arzelà's theorem and strong uniform convergence on bornologies ⋮ Embeddings of bornological universes ⋮ Gap, excess and bornological convergence ⋮ Strong uniform continuity ⋮ Total boundedness and bornologies ⋮ In memoriam: Somashekhar Naimpally (1931--2014). ⋮ A note on convergence of nets of multifunctions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions
• The topology of the \(\rho\)-Hausdorff distance
• Preservation of persistence and stability under intersections and operations. I: Persistence
• Decomposition properties of hyperspace topologies
• Convergence of convex sets and of solutions of variational inequalities
• A Convergence Theory for Saddle Functions
• Isometries for the Legendre-Fenchel Transform
• On Uniform Convergence Structures
• Weak Topologies for the Closed Subsets of a Metrizable Space
• The Infimal Value Functional and the Uniformization of Hit-and-Miss Hyperspace Topologies
• Epigraphical and Uniform Convergence of Convex Functions
• Einige Bemerkungen über der Raum der abgeschlossenen Mengen
• A note on pretopologies
• Convergence of set-valued mappings: Equi-outer semicontinuity

This page was built for publication: Bornological convergences