A quotient topology on the shape homotopy groups

In 2016, the authors considered a topology on the shape homotopy groups of arbitrary topological spaces, π top k (X, x), which make them Hausdorff topological groups. In this talk, we define the kth shape loop space for all k ∈ N and consider a quotient topology on the kth shape group,induced by the kth shape loop space. Then we show that this quotient opology coincides with the above topology