Geodesic
Relaxation of the sequential criteria for continuity and uniform continuity of a real function
The Teaching of Mathematics, XXV (2022) no. 2, p. 116 .

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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.
DOI : 10.57016/TM-SBHR1144
Classification : 97I20, 97I30 I25, I35
Keywords: Continuity, uniform continuity, sequential criterion, Axiom of Choice, global continuity criterion. 
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Spiros Konstantogiannis. Relaxation of the sequential criteria for continuity and uniform continuity of a real function. The Teaching of Mathematics, XXV (2022) no. 2, p. 116 . doi : 10.57016/TM-SBHR1144. http://geodesic.mathdoc.fr/articles/10.57016/TM-SBHR1144/

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