In mathematics, a Suslin representation of a set of reals (more precisely, elements of Baire space) is a tree whose projection is that set of reals. More generally, a subset A of κω is λ-Suslin if there is a tree T on κ × λ such that A = p[''T''].
By a tree on κ × λ we mean a subset T ⊆ ⋃n<ω(κn × λn) closed under initial segments, and p[''T''] = is the projection of T,where [''T''] = is the set of branches through T.
Since [''T''] is a closed set for the product topology on κω × λω where κ and λ are equipped with the discrete topology (and all closed sets in κω × λω come in this way from some tree on κ × λ), λ-Suslin subsets of κω are projections of closed subsets in κω × λω.
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 ωω.