On Strong Small Loop Transfer Spaces Relative to Subgroups of Fundamental Groups
Abstract
Let $H$ be a subgroup of the fundamental group $\pi_{1}(X,x_{0})$. By extending the concept of strong SLT space to a relative version with respect to $H$, strong $H$SLT space, first, we investigate the existence of a covering map for strong $H$SLT spaces. Moreover, we show that a semicovering map is a covering map in the presence of strong $H$SLT property. Second, we present conditions under which the whisker topology agrees with the lasso topology on $\widetilde{X}_{H}$. Also, we study the relationship between open subsets of $\pi_{1}^{wh}(X,x_{0})$ and $\pi_{1}^{l}(X,x_{0})$. Finally, we give some examples to justify the definition and study of strong $H$SLT spaces.
 Publication:

arXiv eprints
 Pub Date:
 November 2017
 DOI:
 10.48550/arXiv.1711.01462
 arXiv:
 arXiv:1711.01462
 Bibcode:
 2017arXiv171101462P
 Keywords:

 Mathematics  Algebraic Topology;
 57M10;
 57M12;
 57M05;
 55Q05
 EPrint:
 16 pages