A fixed point theorem for the pseudo-circle

Let f : C → C be a self-map of the pseudo-circle C . Suppose that C is embedded into an annulus A , so that it separates the two components of the boundary of A . Let F : A → A be an extension of f to A (i.e. F | C = f ). If F is of degree d then f has at least | d − 1 | fixed points. This result generalizes to all plane separating circle-like continua.