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

摘要

Using the topologist sine curve we present a new functorial construction ofcone-like spaces, starting in the category of all path-connected topologicalspaces with a base point and continuous maps, and ending in the subcategory ofall simply connected spaces. If one starts by a noncontractible n-dimensionalPeano continuum for any n>0, then our construction yields a simply connectednoncontractible (n + 1)-dimensional cell-like Peano continuum. In particular,starting with the circle $\mathbb{S}^1$, one gets a noncontractible simplyconnected cell-like 2-dimensional Peano continuum.