Analytic and Luzin spaces (non-separable case)

We introduce the concept of κ-analytic and κ-Luzin spaces as images of complete metric spaces by (disjoint) upper semi-continuous compact-valued correspondences which “preserve discreteness” in some sence (Definition in Section 3.1). The case κ = ω coincides with (Lindelöf) analytic spaces studied by Choquet, the first author and others. The main results are characterizations of uniform analytic spaces in terms of other parametrizations, complete sequences of covers, and Suslin subsets of some product of a compact and a complete metric space (Theorems in Section 3.2 and in Section 4), and characterizations of topological analytic spaces as Suslin subsets of paracompact ?ech-complete spaces (Theorem in Section 5).