Topology and its Applications, ( ISI ), Volume (261), No (1), Year (2019-7) , Pages (29-38)

Title : ( On shape loop spaces )

Authors: Tayyebe Nasri , Behrooz Mashayekhy Fard ,

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In this paper, considering the kth shape loop space Ω ˇ p k -X, x-, for an HPol∗-expansion p : -X, x- → --Xλ, xλ-, [pλλ], Λ- of a pointed topological space -X, x-, first we show that Ω ˇ p k-X, x- is an H-group for every topological space -X, x-. Then we prove that Ω ˇ c k : T op∗ −→ T op∗ is a functor, for all k ∈ N0, where c is the Čech HPol∗-expansion of spaces. Moreover, with some assumptions, we show that if X is πk-shape injective, then X is k-homotopically Hausdorff. Finally, we show that the long exact sequence of shape groups -coarse shape groups- of a pointed pair of certain spaces, is also exact as topological groups.


Shape theory Shape group Topological group Loop space Inverse limit
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author = {Tayyebe Nasri and Mashayekhy Fard, Behrooz},
title = {On shape loop spaces},
journal = {Topology and its Applications},
year = {2019},
volume = {261},
number = {1},
month = {July},
issn = {0166-8641},
pages = {29--38},
numpages = {9},
keywords = {Shape theory Shape group Topological group Loop space Inverse limit},


%0 Journal Article
%T On shape loop spaces
%A Tayyebe Nasri
%A Mashayekhy Fard, Behrooz
%J Topology and its Applications
%@ 0166-8641
%D 2019