Relaxation of the sequential criteria for continuity and uniform continuity of a real function

Abstract

We show how two fundamental sequential criteria for real functions, namely the sequential criterion for continuity and the sequential criterion for uniform continuity, are relaxed. Further, we derive a global continuity criterion, as an immediate consequence of the relaxed sequential criterion for continuity, and a fundamental property of uniformly continuous functions, as an application of the relaxed sequential criterion for uniform continuity.