Open 3-manifolds which are connected sums of closed ones

We consider open, oriented [Formula: see text]-manifolds which are infinite connected sums of closed [Formula: see text]-manifolds. We introduce some topological invariants for these manifolds and obtain a classification in the case where there are only finitely many summands up to diffeomorphism. This result encompasses both the Kneser–Milnor Prime Decomposition Theorem for closed [Formula: see text]-manifolds and the Kerékjártó–Richards classification theorem for open surfaces.