Adjointness of Suspension and Shape Path Functors

Document Type : Original Scientific Paper


1 Department of Pure Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran

2 Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran


In this paper, we introduce a subcategory ∼Sh* of Sh* and obtain some results in this subcategory. First we show that there is a natural bijection Sh(∑(X, x), (Y,y))≅Sh((X,x),Sh((I, Ī),(Y,y))), for every (Y,y)∈ ~Sh* and (X,x)∈ Sh*. By this fact, we prove that for any pointed topological space (X,x) in ∼Sh*ntop(X,x)≅ πn-ktop(Sh((Sk, *),(X,x)), ex), for all 1≤k ≤n-1.


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