A method for constructing ordered continua (Q1062310)

The authors present a method for obtaining rigid ordered continua, i.e. ordered continua which admit no other continuous selfmaps than those which are called necessary (in each case in an appropriate meaning). For instance, an order-homogeneous ordered continuum is constructed which has no other continuous non-increasing selfmaps except those which are constant. A continuum having these properties was constructed for the first time by Shelah in 1976. The authors constructed also an ordered continuum having only so-called canonical retractions as continuous selfmaps; a canonical retraction is a retraction onto a subsegment which maps components of the complement of this subsegment onto its ends.