However, in contrast to the finite-dimensional case, projections need not be continuous in general. If a subspace formula_42 of formula_174 is not closed in the norm topology, then projection onto formula_42 is not continuous. In other words, the range of a continuous projection formula_1 must be a closed subspace. Furthermore, the kernel of a continuous projection (in fact, a continuous linear operator in general) is closed. Thus a "continuous" projection formula_1 gives a decomposition of formula_174 into two complementary "closed" subspaces: formula_198.