Menger manifolds homeomorphic to their 𝑛-homotopy kernels

Abstract

Abstract. We give a necessary and sufficient condition that an (n + l)-dimensional Menger manifold ( /in+1-manifold) is homeomorphic to its n-homotopy kernel. Such a pn+l-manifold is called a p.%¿'-manifold. We also prove the following results:(1) Each homeomorphism between two Z-sets in a /i^1-manifold M extends to an ambient homeomorphism of M onto itself if it is n-homotopic to id in M.