Bulletin of the Australian Mathematical Society

Research Article

A generalized Banach-Mazur theorem

Martin Kleibera1 and W. J. Pervina2

a1 Villanova University, Villanova, Pa. (USA).

a2 Drexel Institute of Technology Philadelphia, Pa. 19104 (USA).


For every infinite cardinal a we let Ca, be the set of all real-valued continuous functions on a product of a closed unit intervals with the supmetric. It is shown that Ca has separability degree a. Further, the classical theorem of Banach and Mazur is generalized by showing that every metric space of separability degree a is isometric to a subspace of ca

(Received March 21 1969)