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New Type of Strongly Continuous Functions In topological Spaces Via δ − β-Open Set

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Abstract (2. Language): 
In this paper we introduce and investigate a new class of strong continuous functions called strongly θ − δ − β-continuous functions by using two new strong forms of δ − β-open sets called δ − β-regular sets and δ − βθ -open sets. This class is a generalization of both strongly θ-e-continuous functions and strongly θ − β-continuous functions. Several new characterizations and fundamental properties concerning strongly θ −δ−β-continuous functions are obtained. Furthermore, the relationships between strongly θ −δ−β-continuous functions and other well-known types of strong continuity are also discussed.
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