Strongly Contractible Polyhedra which are Not Simply Contractible at n Points For any n≥ 2

In this paper we study the concept of strict contractibility defined by E. Michael and construct an example stated in the title of the paper. We also give examples of compact metric spaces in Euclidean 3-space which are simply contractible at n points, for any n ≥ 1, but are not strongly contractible at those points.