# Why should the open mapping theorem be expected?

It is obviously true in the finite case, one circuitious argument being that the exact sequence $0 \to R^k \to R^n \to R^{n-k} \to 0$ splits, and projection maps are open. Can the open mapping theorem be thought of as saying that surjections in the ("isomorphic") category of Banach spaces are like projections, even thought not all exact sequences split (because not all closed subspaces are complemented)?