Dendrites and Light Open Mappings Janusz

  title={Dendrites and Light Open Mappings Janusz},
  author={Janusz J. Charatonik and W. J. CHARATONIK and PAWE L KRUPSKI},
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 ⊂ 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. All spaces considered in this paper are assumed to be metric, and all mappings are continuous. In [3] J. Mioduszewski proved the… CONTINUE READING