Topology and its Applications, ( ISI ), Volume (219), No (1), Year (2017-3) , Pages (17-28)

#### Title : ( Topological coarse shape homotopy groups )

Authors: fateme ghanei , Bibi Hanieh Mirebrahimi Paziquee , Behrooz Mashayekhy Fard , T. Nasri ,

Citation: BibTeX | EndNote

#### Abstract

Cuchillo-Ibanez et al. introduced a topology on the sets of shape morphisms between arbitrary topological spaces in 1999. In this paper, applying a similar idea, we introduce a topology on the set of coarse shape morphisms $Sh^*(X,Y)$, for arbitrary topological spaces $X$ and $Y$. In particular, we can consider a topology on the coarse shape homotopy group of a topological space $(X,x)$, $Sh^*((S^k,*),(X,x))=\check{\pi}_k^{*}(X,x)$, which makes it a Hausdorff topological group. Moreover, we study some properties of these topological coarse shape homotopoy groups such as second countability, movability and in particullar, we prove that $\check{\pi}_k^{*^{top}}$ preserves finite product of compact Hausdorff spaces. Also, we show that for a pointed topological space $(X,x)$, $\check{\pi}_k^{top}(X,x)$ can be embedded in $\check{\pi}_k^{*^{top}}(X,x)$. %the $k$th topological coarse shape homotopy group $\check{\pi}_k^{*^{top}}$ can be considered as a quotient space. %Moreover, we present some basic properties of topological shape homotopy groups.

#### Keywords

, Topological coarse shape homotopy group, Coarse shape group, Shape group, Topological group, Inverse limit.
برای دانلود از شناسه و رمز عبور پرتال پویا استفاده کنید.

@article{paperid:1061046,
author = {Ghanei, Fateme and Mirebrahimi Paziquee, Bibi Hanieh and Mashayekhy Fard, Behrooz and T. Nasri},
title = {Topological coarse shape homotopy groups},
journal = {Topology and its Applications},
year = {2017},
volume = {219},
number = {1},
month = {March},
issn = {0166-8641},
pages = {17--28},
numpages = {11},
keywords = {Topological coarse shape homotopy group; Coarse shape group; Shape group; Topological group; Inverse limit.},
}

%0 Journal Article
%T Topological coarse shape homotopy groups
%A Ghanei, Fateme
%A Mirebrahimi Paziquee, Bibi Hanieh
%A Mashayekhy Fard, Behrooz
%A T. Nasri
%J Topology and its Applications
%@ 0166-8641
%D 2017