Finitely chainable and totally bounded metric spaces: equivalent characterizations

DOI10.1016/j.topol.2016.11.008zbMath1355.54034OpenAlexW2549794962MaRDI QIDQ729832

Somnath Hazra, Subiman Kundu, Manisha Aggarwal

Publication date: 22 December 2016

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

Full work available at URL: https://doi.org/10.1016/j.topol.2016.11.008

zbMATH Keywords

uniformly continuoustotally boundedLipschitz functionLebesgue numberfinitely chainableLipschitz in small function

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Lipschitz (Hölder) classes (26A16) Special maps on metric spaces (54E40) Real-valued functions in general topology (54C30) Functions of one variable (26A99)

Related Items (6)

Unnamed Item ⋮ On Bourbaki-bounded sets on quasi-pseudometric spaces ⋮ Connected \(\epsilon\)-chainable sets and existence results ⋮ Functions that preserve certain classes of sequences and locally Lipschitz functions ⋮ A new type of statistical Cauchy sequence and its relation to Bourbaki completeness ⋮ Locally weak version of the contraction mapping principle

Cites Work

• Uniform continuity of continuous functions of metric spaces
• Atsuji completions: Equivalent characterisations
• More on variants of complete metric spaces
• Locally Lipschitz functions, cofinal completeness, and UC spaces
• Lipschitz-type functions on metric spaces
• Between compactness and completeness
• On uniform spaces where all uniformly continuous functions are bounded
• BORNOLOGIES AND LOCALLY LIPSCHITZ FUNCTIONS
• On Uniform Continuity and Compactness in Metric Spaces
• Which Connected Metric Spaces are Compact?
• New types of completeness in metric spaces
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