Binary tree of finite strings
= Binary tree of finite strings
{title2=$T\subseteq2^{<\omega}$}
= Binary trees of finite strings
{synonym}
A binary tree of finite strings is a set of finite <binary strings> closed under taking prefixes. The empty tree is allowed; a nonempty such tree contains the empty string. Finite nodes may have no infinite extensions. Such presentations describe closed subsets of <Cantor space> through their infinite paths.