Open 3-manifolds which are simply connected at infinity
C. H. Edwards · Proceedings of the American Mathematical Society · 1963
A triangulated open manifold M will be called 1-connected at infinity if each compact subset C of M is contained in a compact polyhedron P in M such that M-P is connected and simply connected. Stallings has shown that, if M is a contractible open combinatorial manifold which is 1-connected at infinity and is of dimension n> 5, then M is piecewise-linearly homeomorphic to Euclidean n-space En [5].