Topology and its Applications, ( ISI ), Volume (158), No (13), Year (2011-6) , Pages (1607-1614)

Title : ( On the homotopy groups of separable metric spaces )

Authors: Fateme Helen Ghane Ostadghassemi , hadi passandideh , Zainab Hamed Labbafian ,

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Abstract

The aim of this paper is to discuss the homotopy properties of locally well-behaved spaces. First, we state a nerve theorem. It gives sufficient conditions under which there is a weak n-equivalence between the nerve of a good cover and its underlying space. Then we conclude that for any (n − 1)-connected, locally (n − 1)-connected compact metric space X which is also n-semilocally simply connected, the nth homotopy group of X, πn(X), is finitely presented. This result allows us to provide a new proof for a generalization of Shelah’s theorem (Shelah, 1988 [18]) to higher homotopy groups (Ghane and Hamed, 2009 [8]). Also, we clarify the relationship between two homotopy properties of a topological space X, the property of being n-homotopically Hausdorff and the property of being n-semilocally simply connected. Further, we give a way to recognize a nullhomotopic 2-loop in 2-dimensional spaces. This result will involve the concept of generalized dendrite which introduce here. Finally, we prove that each 2-loop is homotopic to a reduced 2-loop.

Keywords

, Nerve Homotopy group n, semilocally simply connected space n, connected space Locally n, connected space
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@article{paperid:1022225,
author = {Ghane Ostadghassemi, Fateme Helen and Passandideh, Hadi and Hamed Labbafian, Zainab},
title = {On the homotopy groups of separable metric spaces},
journal = {Topology and its Applications},
year = {2011},
volume = {158},
number = {13},
month = {June},
issn = {0166-8641},
pages = {1607--1614},
numpages = {7},
keywords = {Nerve Homotopy group n-semilocally simply connected space n-connected space Locally n-connected space},
}

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%0 Journal Article
%T On the homotopy groups of separable metric spaces
%A Ghane Ostadghassemi, Fateme Helen
%A Passandideh, Hadi
%A Hamed Labbafian, Zainab
%J Topology and its Applications
%@ 0166-8641
%D 2011

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