On Strong Small Loop Transfer Spaces Relative to Subgroups of Fundamental Groups

2017/11/04 by Seyyed Zeynal Pashaei, Pashaei, S. Z., Behrooz Mashayekhy +3
Mathematics · #55Q05 #57M05 #57M10 #57M12 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1711.01462

openalex publication_date 2017/11/04 · openalex created_date 2017/11/17 · openalex updated_date 2026/07/28

Abstract

Let H be a subgroup of the fundamental group π₁(X,x₀). 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 \widetildeX_H. Also, we study the relationship between open subsets of π₁^wh(X,x₀) and π₁^l(X,x₀). Finally, we give some examples to justify the definition and study of strong H-SLT spaces.

Related

• Small Loop Transfer Spaces with Respect to Subgroups of Fundamental Groups
• On Topologized Fundamental Group and covering spaces of topological groups
• On Topologized Fundamental Groups with Small Loop Transfer Viewpoints
• On quasi-small loop groups
• Making spaces wild (simply-connected case)