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 ${\tilde{X}}_H$. 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.

16 pages

References in corpus (2)

• Topological and uniform structures on universal covering spaces
• On the Spanier Groups and Covering and Semicovering Spaces