Instituto de Matemáticas, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México ; Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Abstract:
It is shown that a metric continuum is a dendrite if and only if for every compact space (continuum) and for every light confluent mapping such that there is a copy of in for which the restriction is a homeomorphism. As a corollary it follows that only dendrites have the lifting property with respect to light confluent mappings. Other classes of mappings are also discussed. This is a continuation of a previous study by the authors (2000), where open mappings were considered.