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.

中文翻译：

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R拓扑空间和SR拓扑空间及其应用

本文介绍了一种基于关系的拓扑空间新概念。这些拓扑空间称为R拓扑空间和SR拓扑空间。验证了这些空间的某些性质以及它们与初始拓扑空间的关系。此外，还验证了它们在定点理论，泛函分析，\（C ^ * \）-代数等中的一些应用。