| Relaxation of the sequential criteria for continuity and uniform continuity of a real function |
| Spiros Konstantogiannis |
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.
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Keywords: Continuity; uniform continuity; sequential criterion; Axiom of Choice; global continuity criterion. |
DOI: 10.57016/TM-SBHR1144 |
Pages: 116$-$121 |
Volume XXV , Issue 2 , 2022 |
