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/lp/de-gruyter/spanier-spaces-and-the-covering-theory-of-non-homotopically-path-9Aw004QwJf
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- Publisher
- de Gruyter
- Copyright
- Copyright © 2013 by the
- ISSN
- 1072-947X
- eISSN
- 1572-9176
- DOI
- 10.1515/gmj-2013-0016
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. In (Topology Appl. 158 (2011), 397–408), Fischer et al. introduced the Spanier group of a based space ( X , x ) which is denoted by . By a Spanier space we mean a space X such that for every . In this paper, first we give an example of Spanier spaces. Then we study the influence of the Spanier group on the 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 establish criteria for the Hausdorffness of topological fundamental groups.
Journal
Georgian Mathematical Journal – de Gruyter
Published: May 1, 2013