A construction of noncontractible simply connected cell-like two-dimensional Peano continua

Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + l)-dimensional celllike Peano continuum. In particular, starting from the circle double-struck S sign ¹, one gets a noncontractible simply connected cell-like 2-dimensional Peano continuum.