Pseudo-contractibility of chainable continua

A space X is called pseudo-contractible if there exist a mapping and points a,b∈C, x0∈X, where C is a continuum, fulfilling H(x,a)=x and H(x,b)=x0. We show that the only (up to homeomorphism) pseudo-contractible chainable continuum is the arc. In particular the pseudo-arc is not pseudo-contractible, which answers a question of W. Kuperberg.