Dendrites and light open mappings

Abstract

It is shown that a metric continuum X is a dendrite if and only if for every compact space Y and for every light open mapping f : Y --> f(Y) such that X subset of f(Y) there is a copy X' of X in Y for which the restriction f\X' : X' --> X is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also obtained.