Infinite path through a binary tree
= Infinite path through a binary tree
{title2=$[T]=\{f\in2^\omega:\forall n\ f\restriction n\in T\}$}
= Infinite paths through a binary tree
{synonym}
An infinite path is a binary <function> all of whose finite prefixes belong to the tree. Its path space $[T]$ is closed in <Cantor space>, since failure is witnessed by one finite prefix outside $T$.