Applications of semi-pre-c-open sets

Semi-pre-c-open sets are a subtle development in topology that has a substantial impact on both theoretical investigations and real-world applications. This study explores the several uses of semi-pre-c-open sets in diverse fields. First, we look into how they may be used to improve the structure of generalized topological spaces and give a more comprehensive framework for studying compactness, continuity, and convergence. A more precise categorization of functions is made possible by semi-pre-c-open sets, opening up new function spaces and expanding on previously established findings. Furthermore, their significant applications in digital topology help to advance digital continuity notions and more efficient picture processing methods. We develop and study semi-pre-c-open sets, a novel class of generalized open sets in a topological space. The semi-pre-open sets class includes this class. It is demonstrated that the topology generated by semi-pre-c-open sets is the same. Semi-pre-c-derived set, semi-pre-c-interior points, semi-pre-c-closure, semi-pre-c-closure, semi-pre-c-frontier, and semi-pre-c-exterior are among the topological aspects of these sets that we present and examine. Using examples and counterexamples, the existence of their relationship is also examined.