Title : ( Adjointness of Suspension and Shape Path Functors )
Authors: Tayyebe nasri , Behrooz Mashayekhy Fard , Bibi Hanieh Mirebrahimi Paziquee ,
Full TextAbstract
In this paper, we introduce a subcategory $\\\\widetilde{Sh}_*$ of Sh$_*$ and obtain some results in this subcategory. First we show that there is a natural bijection $Sh (\\\\Sigma (X, x), (Y,y))\\\\cong Sh((X,x),Sh((I, \\\\dot{I}),(Y,y)))$, for every $(Y,y)\\\\in \\\\widetilde{Sh}_*$ and $(X,x)\\\\in Sh_*$. By this fact, we prove that for any pointed topological space $(X,x)$ in $\\\\widetilde{Sh}_*$, $\\\\check{\\\\pi}_n^{top}(X,x)\\\\cong \\\\check{\\\\pi}_{n-k}^{top}(Sh((S^k, *),(X,x)), e_x)$, for all $1\\\\leq k \\\\leq n-1$.
Keywords
, shape category, topological shape homotopy group, shape group, suspensions
@article{paperid:1084689,
author = {Tayyebe Nasri and Mashayekhy Fard, Behrooz and Mirebrahimi Paziquee, Bibi Hanieh},
title = {Adjointness of Suspension and Shape Path Functors},
journal = {Mathematics Interdisciplinary Research},
year = {2021},
volume = {6},
number = {1},
month = {April},
issn = {2538-3639},
pages = {23--33},
numpages = {10},
keywords = {shape category; topological shape homotopy group; shape group; suspensions},
}
%0 Journal Article
%T Adjointness of Suspension and Shape Path Functors
%A Tayyebe Nasri
%A Mashayekhy Fard, Behrooz
%A Mirebrahimi Paziquee, Bibi Hanieh
%J Mathematics Interdisciplinary Research
%@ 2538-3639
%D 2021
