A STUDY OF FUNCTION DIFFERENTIABILITY IN TERMS OF CONTINUITY UNDER SELECTED TOPOLOGICAL STRUCTURES

ABSTRACT

This research paper explores the relationship between function differentiability and continuity within specific topological structures. The aim is to investigate the conditions under which differentiability implies continuity and vice versa, focusing on selected topological spaces. By examining various properties and concepts related to differentiability and continuity, we aim to establish a deeper understanding of their interplay and uncover any additional implications that arise within these chosen topological structures. This study has important implications for the field of mathematical analysis and can provide valuable insights into the nature of functions within specific topological contexts.

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