Uniform continuity and a new bornology for a metric space

DOI10.1007/s11228-017-0429-4zbMath1422.54019OpenAlexW2623032243MaRDI QIDQ1745912

M. Isabel Garrido, Ana S. Meroño, Gerald A. Beer

Publication date: 18 April 2018

Published in: Set-Valued and Variational Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11228-017-0429-4

zbMATH Keywords

continuous functionLipschitz functionCauchy continuous functionuniformly continuous functionbornologyring of functionsrelatively compact settotally bounded setBourbaki bounded setUC-spaceinfinitely nonuniformly isolated set

Mathematics Subject Classification ID

Complete metric spaces (54E50) Function spaces in general topology (54C35) Metric spaces, metrizability (54E35) Lipschitz (Hölder) classes (26A16) Bornologies and related structures; Mackey convergence, etc. (46A17)

Related Items (9)

Stability of Lipschitz-type functions under pointwise product and reciprocation ⋮ Uniform split continuity ⋮ McShane's extension theorem revisited ⋮ Functions that preserve certain classes of sequences and locally Lipschitz functions ⋮ Preservation of uniform continuity under pointwise product ⋮ Strong Whitney and strong uniform convergences on a bornology ⋮ On boundedly compact metrics and UC metrics ⋮ Real-valued Lipschitz functions and metric properties of functions ⋮ Quiz your maths: Do the uniformly continuous functions on the line form a ring?

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