$delta$-Quasi Cauchy Sequences
Huseyin Cakalli

TL;DR
This paper introduces and studies the concepts of second forward continuity and second forward compactness, extending existing ideas of forward continuity and compactness by involving second differences, and explores their properties and implications.
Contribution
It defines second forward continuity and second forward compactness, analyzing their properties and how they relate to existing notions of sequence convergence and set compactness.
Findings
Established the definitions of second forward continuity and compactness.
Proved theorems relating second forward concepts to classical notions.
Explored the impact of different convergence definitions on these properties.
Abstract
Recently, a concept of forward continuity and a concept of forward compactness are introduced in the senses that a function is forward continuous if whenever ,\; and a subset of is forward compact if any sequence of points in has a subsequence of the sequence such that where . These concepts suggest us to introduce a concept of second forward continuity in the sense that a function is second forward continuous if whenever , and a subset of is second forward compact if whenever is a sequence of points in there is a subsequence…
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topology and Set Theory · Advanced Banach Space Theory
