On the uniform approximation of Cauchy continuous functions

DOI10.1016/j.topol.2016.04.017zbMath1342.41038OpenAlexW2390214663MaRDI QIDQ290605

M. Isabel Garrido, Gerald A. Beer

Publication date: 3 June 2016

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

Full work available at URL: https://doi.org/10.1016/j.topol.2016.04.017

zbMATH Keywords

uniform approximationlocally Lipschitz functionCauchy sequenceCauchy continuous functionCauchy-Lipschitz functionLipschitz in the small function

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Classical Banach spaces in the general theory (46B25) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Banach sequence spaces (46B45)

Related Items

Cauchy-subregular functions vis-à-vis different types of continuity, Split continuity, Stability of Lipschitz-type functions under pointwise product and reciprocation, Split Lipschitz-type functions, Functions that preserve certain classes of sequences and locally Lipschitz functions, Cofinal completion vis-á-vis Cauchy continuity and total boundedness, Cofinal completeness vis-á-vis hyperspaces, Functions that are Lipschitz in the small, Real-valued Lipschitz functions and metric properties of functions, On some Lipschitz-type functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniform continuity of continuous functions of metric spaces
• Atsuji completions: Equivalent characterisations
• Lectures on analysis on metric spaces
• Approximation of continuous functions by Lipschitz functions
• Homomorphisms on function lattices
• Modern analysis and topology
• Locally Lipschitz functions, cofinal completeness, and UC spaces
• Lipschitz-type functions on metric spaces
• Between compactness and completeness
• Rings of functions with certain Lipschitz properties
• BORNOLOGIES AND LOCALLY LIPSCHITZ FUNCTIONS
• Cofinal completeness of the Hausdorff metric topology
• More about metric spaces on which continuous functions are uniformly continuous
• Mappings that preserve Cauchy sequences
• Elements of Lipschitz topology
• Rings of functions in Lipschitz topology