  Let X and Y be oriented topological manifolds of dimension n + 2, and let K
and J be connected, locally-flat, oriented, n-dimensional submanifolds of X and
Y. We show that up to orientation preserving homeomorphism there is a
well-defined connected sum K # J in X # Y. For n = 1, the proof is classical,
relying on results of Rado and Moise. For dimensions n = 3 and n > 5, results
of Edwards-Kirby, Kirby, and Kirby-Siebenmann concerning higher dimensional
topological manifolds are required. For n = 2, 4, and 5, Freedman and Quinn's
work on topological four-manifolds is needed. The truth of the corresponding
statement for higher codimension seems to be unknown.
