  The path spaces of a directed graph play an important role in the study of
graph $\css$. These are topological spaces that were originally constructed
using groupoid and inverse semigroup techniques. In this paper, we develop a
simple, purely topological, approach to this construction, based on Tychonoff's
theorem. In fact, the approach is shown to work even for higher dimensional
graphs satisfying the finitely aligned condition, and we construct the groupoid
of the graph. Motivated by these path space results, we prove a Tychonoff
theorem for an infinite, countable product of locally compact spaces. The main
idea is to include certain finite products of the spaces along with the
infinite product. We show that the topology is, in a reasonable sense, a
pointwise topology.
