Metric, stratifiable and uniform spaces of <i>G</i>-permutation degree
R. B. BeshimovNational University of Uzbekistan named after Mirzo Ulugbek str. University Tashkent UzbekistanDimitrios N. GeorgiouDepartment of Mathematics University of Patras Patras GreeceF. SeretiDepartment of Mathematics University of Western Macedonia Kastoria GreeceRustam M. ZhuraevNational University of Uzbekistan named after Mirzo Ulugbek str. University Tashkent Uzbekistan
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In this paper, we study the space SPGn $\begin{array} \displaystyle SP_{G}^{n} \end{array}$ X of G -permutation degree. Especially, new properties of this space are investigated. We study its metrazibility, semi-metrazibility, stratifiability, semi-stratifiability and uniformizability. Moreover, we study the uniform space (SPGnX,SPGnΥ), $\begin{array} \displaystyle (SP_{G}^{n}X, SP_{G}^n\Upsilon), \end{array}$ investigating when this space is totally bounded ( ω -bounded). Finally, a study of universal elements in classes of spaces that are presented in this article, and related open questions complete this paper.
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