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 κω is λ-Suslin if there is a tree T on κ × λ such that A = p.
By a tree on κ × λ we mean here a subset T of the union of κi × λi for all i ∈ N.
Here, p = is the projection of T,
where = is the set of branches through T.
Since is a closed set for the product topology on κω × λω where κ and λ are equipped with the discrete topology, 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.
