A decomposition of En (n≥3) into points and a null sequence of cellular sets

Abstract

The non-manifold dog bone space of W.T. Eaton is modified to obtain a decomposition of Euclidean n-space, n≥3, into points and a null sequence of cellular sets so that the resulting decomposition space is not a manifold. Our construction follows a procedure given by R.J. Daverman who has proved this result for n≥5. Our construction has the advantage of working in all possible dimensions including the previously unknown dimension 4.