Delta-epsilon functions and uniform continuity on metric spaces
C\'esar Adolfo Hern\'andez Melo
TL;DR
This paper introduces an explicit formula for the greatest delta-epsilon function of continuous functions on metric spaces, providing a new method to analyze uniform continuity with illustrative examples.
Contribution
It presents a novel explicit formula for delta-epsilon functions and a new approach to assess uniform continuity in metric spaces.
Findings
Derived an explicit formula for the greatest delta-epsilon function.
Provided a new analytical method for uniform continuity.
Included several illustrative examples.
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.
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Taxonomy
TopicsFunctional Equations Stability Results · Fixed Point Theorems Analysis · Advanced Topology and Set Theory