Concepts of generalized hyperconnected sets and components established in topological spaces, suggesting new properties and conditions for connectedness.
This paper introduces the notion of generalized hyperconnected sets in topological spaces using Levine’s concept of generalized closed sets. We define generalized hyperconnected sets and generalized hyperconnected components and study their fundamental properties. Furthermore, we provide necessary conditions for a topological space to be generalized hyperconnected. The relationship between this type of connectedness and other types is also presented. Several results concerning these new concepts are obtained and proven.
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Amna M. A. Ahmed (2025) studied this question.
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