Expansive homeomorphisms and plane separating continua

A homeomorphism h : X → X 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 ( h n ( x ) , h n ( 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.