Shape Loop Space of Pro-discrete Spaces
عنوان مقاله: Shape Loop Space of Pro-discrete Spaces
شناسه ملی مقاله: JR_CJMS-11-1_021
منتشر شده در در سال 1401
شناسه ملی مقاله: JR_CJMS-11-1_021
منتشر شده در در سال 1401
مشخصات نویسندگان مقاله:
Tayyebe Nasri - Department of Pure Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran
خلاصه مقاله:
Tayyebe Nasri - Department of Pure Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran
In this paper, considering the kth shape loop space \check{\Omega}_{k}^{\mathbf{p}}(X,x), for an HPol_*-expansion \mathbf{p}:(X,x)\rightarrow ((X_{\lambda},x_{\lambda}),[p_{\lambda\lambda'}],\Lambda) of a pointed topological space (X,x), first we prove that \check{\Omega}_{k} commutes with the product under some conditions and then we show that \check{\Omega}_k^{\mathbf{p}}(X,x)\cong \displaystyle{\lim_{\leftarrow}\check{\Omega}_k^{\mathbf{p}}(X_i,x_i)}, for a pro-discrete space (X,x)=\displaystyle{\lim_{\leftarrow}(X_i,x_i)} of compact polyhedra. Finally, we conclude that these spaces are metric, second countable and separable.
کلمات کلیدی: Shape theory, Inverse limit, Loop space
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1616751/