Embed connected sum of submanifolds in the ambient manifold

The book Differential Manifolds by Kosinski claimed we can embed the connected sum of two submanifolds of codimension $>1$ into the ambient manifold. I am wondering why we need the extra condition $>1$ at here. At least in dimension 1-3 I could not find a counter example. On the other hand I also do not know how to prove this rigorously enough. So I venture to ask.

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