Cakalli H.2024-07-122024-07-1220181571-065310.1016/j.endm.2018.05.0062-s2.0-85048406976https://dx.doi.org/10.1016/j.endm.2018.05.006https://hdl.handle.net/20.500.12415/7925In this paper, we introduce and investigate the concepts of down continuity and down compactness. A real valued function f on a subset E of R, the set of real numbers is down continuous if it preserves downward half Cauchy sequences. It turns out that the set of down continuous functions is a proper subset of the set of continuous functions. © 2018 Elsevier B.V.eninfo:eu-repo/semantics/closedAccesscontinuitySequencesseriessummabilityArticle35Q43167