Abstract:
Openness of induced mappings between hyperspaces of continua is studied. In particular we investigate continua X such that if for a mapping f:X --> Y the induced mapping C(f):C(X) --> C(Y) is open, then f is a homeomorphism. It is shown that, besides hereditarily locally connected continua, ail fans have this property, while some Cartesian products do not have it. If f: X x Y --> X denotes the natural projection, then openness of C(f) implies that X is hereditarily unicoherent. The equivalence holds for dendrites. Some new characterizations of these curves are obtained. (C) 1999 Elsevier Science B.V. All rights reserved.