Abstract:In this paper, we investigate the concepts of downward continuity and upward continuity. A real valued function on a subset E of R, the set of real numbers, is downward continuous if it preserves downward quasi-Cauchy sequences; and is upward continuous if it preserves upward quasi-Cauchy sequences, where a sequence (x k) of points in R is called downward quasi-Cauchy if for every ε > 0 there exists an n 0 ∈ N such that x n+1 − x n < ε for n ≥ n 0 , and called upward quasi-Cauchy if for every ε > 0 there exist… Show more
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