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Spanier spaces and the covering theory of non-homotopically path Hausdorff spaces
-
Behrooz Mashayekhy
,
Ali Pakdaman
Veröffentlicht/Copyright:
15. Mai 2013
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.
Keywords: Covering space; Spanier group; Spanier space; homotopically path Hausdorffness; small loop homotopically Hausdorffness; shape injectivity
Received: 2012-06-16
Revised: 2012-10-31
Accepted: 2013-04-07
Published Online: 2013-05-15
Published in Print: 2013-05-01
© 2013 by Walter de Gruyter Berlin Boston
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Schlagwörter für diesen Artikel
Covering space;
Spanier group;
Spanier space;
homotopically path Hausdorffness;
small loop homotopically Hausdorffness;
shape injectivity
Artikel in diesem Heft
- Masthead
- Fixed points of asymptotically regular mappings in complex-valued metric spaces
- Coverings of internal groupoids and crossed modules in the category of groups with operations
- A new study on almost increasing and quasi-monotone sequences
- On precompact sets in spaces Cc(X)
- Weighted boundedness for Toeplitz type operators related to Riesz transforms of the Schrödinger operator
- Sums of absolutely nonmeasurable functions
- Symmetry of an integral equation with Bessel potential in ℝn+
- Spanier spaces and the covering theory of non-homotopically path Hausdorff spaces
- On the maximal operator of Marcinkiewicz–Fejér means of the two-dimensional Walsh–Kaczmarz system
- Hofer type geometry on the space of Legendrian submanifolds of a contact manifold
- Initial problems for hyperbolic functional differential systems
- Approximation by complex q-Bernstein–Schurer operators in compact disks
- On some properties of conjugate trigonometric Fourier series
