Pseudo-contractibility of chainable continua

A space X is called pseudo-contractible if there exist a mapping H : X × C → X and points a , b ∈ C , x 0 ∈ X , where C is a continuum, fulfilling H ( x , a ) = x and H ( x , b ) = x 0 . 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.