In mathematics, especially mathematical logic and set theory, a branch of a tree T is a map f such that ∀n : f (n) ∈ T.
By a tree on a product set κ_{1} ×···× κ_{p} we mean here a subset of the union of κ_{1}^{i}×···×κ_{p}^{ i} for all i < ω,
closed under initial segments, and the set of branches of such a tree is then more explicitly the set
This is a closed set for the usual product topology (see AD plus).
