(ex.4.16. from chapter 3 of "Advanced Calculus" by L.H.Loomis, S.Sternberg)
Let N be a closed subspace of a normed linear space, and suppose that N has a finite-dimensional complement in the purely algebraic sense. Prove that then V is the norm direct sum M(+)N.
The authors advise using the fact that if V and W are fin.-dim. normed linear spaces then every mapping in Hom(V, W) is bounded, and also using the projection P of V onto N along M.
The problem is that I don't understand what the "norm direct sum" is, and so I don't know what exactly I have to prove. There was no such definition in the theoretical material of the chapter. I could suggest what it means if there was, for example, "a norm on a direct sum", or something like that. But it's surely a different concept. And when I Google it the results are not what I'm looking for. Could you please explain what that concept means? Maybe it's just a mistake in the exercise?