Perfect path space
= Perfect path space
A nonempty path space $[T]$ is perfect if it has no isolated points: for every path and every finite prefix of it there is a different path sharing that prefix. This property of the closed subset of <Cantor space> does not imply that its particular finite-string presentation has no dead ends. Requiring every finite node to extend to incompatible nodes is the stronger pruned-tree convention for a perfect tree.