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R-topological spaces and SR-topological spaces with their applications

Abstract

In this paper, a new and applied concept of topological spaces based upon relations is introduced. These topological spaces are called R-topological spaces and SR-topological spaces. Some of the properties of these spaces and their relationship with the initial topological space are verified. Moreover, some of their applications for example in fixed point theory, functional analysis, \(C^*\)-algebras and etc, is verified.

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Acknowledgements

The authors would like to thank the anonymous referee for his/her comments that helped us improve this article.

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Correspondence to Hamidreza Rahimi.

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Khalehoghli, S., Rahimi, H. & Eshaghi Gordji, M. R-topological spaces and SR-topological spaces with their applications. Math Sci 14, 249–255 (2020). https://doi.org/10.1007/s40096-020-00338-5

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  • DOI: https://doi.org/10.1007/s40096-020-00338-5

Keywords

  • Topological space
  • Net
  • R-topological space
  • SR-topological space
  • Fixed point