A quotient topology on the shape homotopy groups

In 2016, the authors considered a topology on the shape homotopy groups of arbitrary topological spaces, $\check{\pi}_k^{top}(X,x)$, which make them Hausdorff topological groups. In this talk, we define the $k^{th}$ shape loop space for all $k\in \mathbb{N}$ and consider a quotient topology on the $k^{th}$ shape group, induced by the $k^{th}$ shape loop space. Then .we show that this quotient topology coincides with the above topology