On ϖ-ν-Continuous Functions in Topological Spaces
DOI:
https://doi.org/10.31642/JoKMC/2018/130208Keywords:
ϖ-ν-continuity, ϖ-closure, ν-open sets, hybrid generalized continuity, generalized closed sets.Abstract
In this work, we introduce and investigate the concept of ϖ-ν-continuous functions in topological spaces. A function is defined as ϖ-ν-continuous if the inverse image of every closed set is a ϖ-ν-closed set, meaning that its ϖ-type closure remains confined within each ν-type open superset. The concept of ϖ-ν-continuity bridges ϖ-type and ν-type continuity, serving as a generalization of both concepts. We examine the fundamental properties of ϖ-ν-continuous functions and establish related decomposition theorems. Furthermore, we provide illustrative examples, including one in a four-point space, to demonstrate the concepts. Importantly, we explore the practical applications of ϖ-ν-continuous functions in fields such as digital image analysis, rough set theory, and topological data representation. This opens new possibilities for applying generalized continuity patterns in real-world computing environments using ϖ-ν-continuous functions and topological spaces.
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