Delta-epsilon functions and uniform continuity on metric spaces

2017/10/09 by César A. Hernández Melo, Melo, César Adolfo Hernández
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Equations Stability Results #General Mathematics (math.GM)

paper · pdf · doi:10.48550/arxiv.1710.04070

openalex publication_date 2017/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under certain general conditions, an explicit formula to compute the greatest delta-epsilon function of a continuous function is given. From this formula, a new way to analyze the uniform continuity of a continuous function is given. Several examples illustrating the theory are discussed.

Related

• Universally uniformly continuous metric spaces
• Functions that preserve totally bounded sets vis-á-vis stronger notions of continuity
• From Uniform Continuity to Absolute Continuity
• Absolutely continuous functions with values in metric spaces
• Remarks on Uniformly Symmetrically Continuous Functions