The classical theory of analytic sets works well in metric spaces, but the analytic sets themselves are automatically separable. The theory of K-analytic sets, developed by Choquet, Sion, Frolik and others, works well in Hausdorff spaces, but the K-analytic sets themselves remain Lindelof. The theory of k-analytic sets developed by A. H. Stone and R. W. Hansell works well in non-separable metric spaces, especially in the special case, when k is ℵ0, with which we shall be concerned, see [9, 10 and 16–20]. Of course the k-analytic sets are metrizable. For accounts of these theories, see, for example, .