This study defines a new ~topological space using a novel ~operator, suggesting new properties in cluster systems.
In this paper, we introduced a new type of operators, which we called ~-operator by cluster system, and studied its properties without conditions and with certain conditions. Through our study of this operator, we defined a new topology, which we called ~-topological space, since it does not, in general, constitute a regular topological space. We also presented ~-interior points, ~-closure, ~-exterior points and reviewed some theories and examples about this concept.
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Hadi et al. (2025) studied this question.
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