  For an $\alpha$-expansive homeomorphism of a compact space we give an
elementary proof of the following well-known result in topological dynamics: A
sufficient condition for the homeomorphism to have the shadowing property is
that it has the $\alpha$-shadowing property for one-jump pseudo orbits (known
as the local product structure property). The proof relies on a reformulation
of the property of expansiveness in terms of the pseudo orbits of the system.
