Abstract
In this paper, we investigate the concept of upward continuity. A real valued function on a subset E of R, the set of real numbers is upward continuous if it preserves upward quasi Cauchy sequences in E, where a sequence (xk) of points in R is called upward quasi Cauchy if for every ε > 0 there exists a positive integer n0 such that xn − xn+1 < ε for n ≥ n0. It turns out that the set of upward continuous functions is a proper subset of the set of continuous functions.
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