On the Singular Homology of One Class of Simply-connected Cell-like Spaces

In our earlier papers we constructed examples of 2-dimensional nonaspherical simply-connected cell-like Peano continua, called Snake space. In the sequel we introduced the functor SC(−,−) defined on the category of all spaces with base points and continuous mappings. For the circle S1, the space \({SC(S^1, {_{*}})}\) is a Snake space. In the present paper we study the higher-dimensional homology and homotopy properties of the spaces \({SC(Z, {_{*}})}\) for any path-connected compact spaces Z.