The end point compactification of manifolds

Abstract

Introduction^ This paper originated in trying to show that the one point compactification of an orientable generalized ^-manifold (n-grn) with cohomology isomorphic to Euclidean n-space was an orientable n-gm. Heretofore, in papers on transformation groups where this was relevant, it was stated as an extra assumption. 1 The solution to this problem is given as a corollary to the main theorems which characterize the orientable (or locally orientable) generalized manifolds whose Freudenthal end point compactification is again an orientable (or locally orientable) generalized ^-manifold (see 4.5 and 4.13). In the first section we give a new characterization of the Freudenthal end point compactification in terms of inverse limits. We show as in Specker [10] that a certain O-dimensional cohomology group measures the extent of this compactification.