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 ...

For continua X and Y it is shown that if the projection f : X x Y --> X has its induced mapping C(f) open, then X is C-smooth. As a corollary, a characterization of dendrites in these terms is obtained.