  Infinite graphs are finitary in the sense that their points are connected via
finite paths. So what would an infinitary generalization of finite graphs look
like? Usually this question is answered with the aid of topology, e.g. in the
case of graph-like spaces. Here we introduce a more combinatorial answer, which
we call path space, and prove a version of Menger's theorem for it. Since there
are many topological path-like objects which induce path spaces, this result
can be applied in a variety of settings.
