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...

Let H be a subgroup of the fundamental group π1(X,x0). In this paper, first, we give a positive answer to a problem presented by Brodskiy et al. in [8, Problem 4.8]. Second, by extending the concept of strong SLT space to ...

Let $H$ be a subgroup of $\\pi_{1}(X,x_{0})$. In this paper, we extend the concept of $X$ being SLT space to $H$-SLT space at $x_0$. First, we show that the fibers of the endpoint projection $p_{H}:\\widetilde {X}_{H}\\rightarrow ...