arXiv subjects
Publications and source records attributed to Fateme Ghanei.
In this paper, using the notions graphs, core graphs, immersions and covering maps of graphs, introduced by Stallings in 1983, we prove the Burnside condition for the intersection of subgroups of free groups with Burnside condition.
Uchillo-Ibanez et al. introduced a topology on the sets of shape morphisms between arbitrary topological spaces in 1999. In this paper, applying a similar idea, we introduce a topology on the set of coarse shape morphisms $Sh^*(X,Y)$, for arbitrary topological spaces $X$ and $Y$. In particular, we can consider a topology on the coarse shape homotopy group of a topological space $(X,x)$, $Sh^*((S^k,*),(X,x))=\checkπ_k^{*}(X,x)$, which makes it a Hausdorff topological group. Moreover, we study some properties of these topological coarse shape homotopoy groups such as second countability, movability and in particullar, we prove that $\checkπ_k^{*^{top}}$ preserves finite product of compact Hausdorff spaces. Also, we show that for a pointed topological space $(X,x)$, $\checkπ_k^{top}(X,x)$ can be embedded in $\checkπ_k^{*^{top}}(X,x)$.