Hey everybody, I was hoping if somebody could help me out with the terminology. I've found that the "end of a manifold" is a function asigning to each compact set K a conected component e(K) of the complement of K. I am trying to understand Gompf's article "three exotic $R^{4}$ 's and other anomalies" and he quotes a theorem of Freedman (Corollary 1.2 in "The topology of 4-dimensional manifolds) saying "Any open 4-manifold M with $\pi_{1}(M)$, $H_{1}(M)$ and end collared (topologically) by $S^{3}\times R$ is homeomorphic to $R^{4}$". How can a function be homeomorphic to something? Im interpreting this as end meaning the "hypothetical boundary" of the manifold. Thanks in advance.