Abstract
Using the notion of \(\delta \beta \)-open set, we intend to do more research on rough continuous functions. The ideas of \(\delta \beta \)-totally rough continuous functions and \(\delta \beta \)-strongly rough continuous functions are proposed and researched. The notions of \(\delta \beta \)-internally and \(\delta \beta \)-totally functions are discussed, as well as some of their characterizations. Finally, the composition of \(\delta \beta \)-internally and totally functions is discussed.
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