Georgian Mathematical Journal, ( ISI ), Volume (20), No (2), Year (2013-4) , Pages (303-317)

Title : ( Spanier spaces and covering theory of non-homotopically path Hausdorff spaces )

Authors: Behrooz Mashayekhy Fard , Ali Pakdaman , Hamid Torabi Ardakani ,

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Abstract

H. Fischer et al. (Topology and its Application, 158 (2011) 397-408.) introduced the Spanier group of a based space $(X,x)$ which is denoted by $\psp$. By a Spanier space we mean a space $X$ such that $\psp=\pi_1(X,x)$, for every $x\in X$. In this paper, first we give an example of Spanier spaces. Then we study the influence of the Spanier group on covering theory and introduce Spanier coverings which are universal coverings in the categorical sense. Second, we give a necessary and sufficient condition for the existence of Spanier coverings for non-homotopically path Hausdorff spaces. Finally, we study the topological properties of Spanier groups and find out a criteria for the Hausdorffness of topological fundamental groups.

Keywords

Covering space; Spanier group; Spanier space; Homotopically path Hausdorffness; Small loop homotopically Hausdorffness; Shape injectivity.
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@article{paperid:1035050,
author = {Mashayekhy Fard, Behrooz and Ali Pakdaman and Torabi Ardakani, Hamid},
title = {Spanier spaces and covering theory of non-homotopically path Hausdorff spaces},
journal = {Georgian Mathematical Journal},
year = {2013},
volume = {20},
number = {2},
month = {April},
issn = {1072-947X},
pages = {303--317},
numpages = {14},
keywords = {Covering space; Spanier group; Spanier space; Homotopically path Hausdorffness; Small loop homotopically Hausdorffness; Shape injectivity.},
}