On Topologized Fundamental Groups with Small Loop Transfer Viewpoints

2017/08/08 by Jamali, Noorollah, Mashayekhy, Behrooz, Torabi, Hamid +2 · 1 citation
#54H11 #55P35 #57M05 #57M12 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.02606

Abstract

In this paper, by introducing some kind of small loop transfer spaces at a point, we study the behavior of topologized fundamental groups with the compact-open topology and the whisker topology, π₁^qtop(X,x₀) and π₁^wh(X,x₀), respectively. In particular, we give necessary or sufficient conditions for coincidence and being topological group of these two topologized fundamental groups. Finally, we give some examples to show that the reverse of some of these implications do not hold, in general.

Cited by

• Comparison of Topologies on Fundamental Groups with Subgroup Topology Viewpoint

Related

• On Topologized Fundamental Group and covering spaces of topological groups
• Small Loop Transfer Spaces with Respect to Subgroups of Fundamental Groups
• On The Whisker Topology
• On Strong Small Loop Transfer Spaces Relative to Subgroups of Fundamental Groups
• On quasi-small loop groups