 Non-separable Banach spaces cannot embed isometrically in the separable space , but for every Banach space , one can find a compact Hausdorff space and an isometric linear embedding of into the space of scalar continuous functions on .The simplest choice is to let be the unit ball of the continuous dual , equipped with the w*-topology.This unit ball is then compact by the Banach–Alaoglu theorem.