Generalizations of Rough Functions in Topological Spaces by Using Pre-Open Sets ()

Amgad S. Salama, Hassan M. Abu-Donia

Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

**DOI: **10.4236/jilsa.2012.42012
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Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

Functions are a means to link or transport from a world to another world may be similarly or completely different from the other world. In this paper we addressed the issue of rough functions and the possibility of transfer it from the real line to the topological abstract view that can be applied to intelligent information systems. The rough function approach has not been studied much specially from a topological point of view. Here we developed a new type of topological generalizations of rough functions with reference to how it is used in medical applications. Considering that the function is in the original a relation can be based on a review of all circular functions from the perspective of relations. Accordingly, the dream that the generalizations of rough functions are transferred to all papers prior to a comprehensive computer application.

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A. Salama and H. Abu-Donia, "Generalizations of Rough Functions in Topological Spaces by Using Pre-Open Sets," *Journal of Intelligent Learning Systems and Applications*, Vol. 4 No. 2, 2012, pp. 127-134. doi: 10.4236/jilsa.2012.42012.

Conflicts of Interest

The authors declare no conflicts of interest.

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