Acta Mathematica Vietnamica
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On Topologized Fundamental Groups with Small Loop Transfer Viewpoints
Noorollah Jamali , Behrooz Mashayekhy , Hamid Torabi , Seyyed Zeynal Pashaei , Mehdi Abdullahi Rashidpp. 711-722
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, $\pi _{1}^{qtop}(X,x_{0})$ and $\pi _{1}^{wh}(X,x_{0})$, respectively. In particular, we give necessary or sufficient conditions for equality and being topological group of these two topologized fundamental groups. Finally, we give some examples to show that the converse of some of these implications do not hold, in general.