Expansive homeomorphisms and plane separating continua

A homeomorphism is expansive provided that there exists a constant c>0 and for every x,y∈X there exists an integer n, dependent only on x and y, such that d(hn(x),hn(y))>c. It is shown that if X is a 1-dimensional continuum that separates the plane into 2 pieces, then h cannot be expansive.