Total boundedness and bornologies

DOI10.1016/j.topol.2008.12.030zbMath1167.54008OpenAlexW1983878843MaRDI QIDQ1013812

Sandro Levi, Gerald A. Beer

Publication date: 23 April 2009

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2008.12.030

zbMATH Keywords

total boundednessbornology

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (25)

Cauchy-subregular functions vis-à-vis different types of continuity ⋮ Representations of bornologies ⋮ Homomorphisms on Topological Groups from the Perspective of Bourbaki-boundedness ⋮ Maps that preserve left (right) $K$-Cauchy sequences ⋮ BORNOLOGIES AND LOCALLY LIPSCHITZ FUNCTIONS ⋮ Split continuity: a different perspective ⋮ \(L\)-valued bornologies on powersets ⋮ 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 ⋮ Unnamed Item ⋮ The structure of extended real-valued metric spaces ⋮ The Alexandroff one-point compactification as a prototype for extensions ⋮ Graphical convergence of continuous functions ⋮ Complete metrizability of topologies of strong uniform convergence on bornologies ⋮ On realcompactifications defined by bornologies ⋮ Strong Whitney and strong uniform convergences on a bornology ⋮ Bornologies, topological games and function spaces ⋮ Arzelà's theorem and strong uniform convergence on bornologies ⋮ Embeddings of bornological universes ⋮ Gap, excess and bornological convergence ⋮ Strong uniform continuity

Cites Work

• Atsuji completions: Equivalent characterisations
• Embeddings of bornological universes
• The topology of the \(\rho\)-Hausdorff distance
• Extensions of unbounded topological spaces
• Characterizations of Banach spaces via convex and other locally Lipschitz functions
• Bornological convergences
• The Wijsman and Attouch-Wets topologies on hyperspaces revisited
• On metric boundedness structures
• \(\mathcal S\)-topologies and bounded convergences
• Boundedness in a topological space
• More about metric spaces on which continuous functions are uniformly continuous
• Uniform Continuity on Bounded Sets and the Attouch-Wets Topology
• Boundedness, one-point extensions and B-extensions
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