Suslin representation

In mathematics, a Suslin representation of a set of reals is a tree whose projection is that set of reals. More generally, a subset A of κ^ω is λ-Suslin if there is a tree T on κ × λ such that A = p.
By a tree on κ × λ we mean a subset T ⊆ ⋃_n<ω closed under initial segments, and p = is the projection of T,
where = is the set of branches through T.
Since is a closed set for the product topology on κ^ω × λ^ω where κ and λ are equipped with the discrete topology, λ-Suslin subsets of κ^ω are projections of closed subsets in κ^ω × λ^ω.
When one talks of Suslin sets without specifying the space, then one usually means Suslin subsets of R, which descriptive set theorists usually take to be the set ω^ω.