 Every real, separable Banach space is isometrically isomorphic to a closed subspace of , the space of all continuous functions from the unit interval into the real line.On the one hand, the Banach–Mazur theorem seems to tell us that the seemingly vast collection of all separable Banach spaces is not that vast or difficult to work with, since a separable Banach space is "only" a collection of continuous paths.On the other hand, the theorem tells us that is a "really big" space, big enough to contain every possible separable Banach space.