ON CONTINUOUS IMAGES OF RADON-NIKOD YM COMPACT SPACES THROUGH THE METRIC CHARACTERIZATION

Through basic properties relating to fragmenta- tion, lower semicontinuity and evaluations along nite paths, we show a necessary and sucient condition for the invari- ance of the RN compact spaces under continuous mappings. We observe a simple proof for this invariance in the case of 0-dimensional images. We apply the characterization theo- rem to conditions of 0-dimensionality and of metrizability of the closure of the set of nontrivial bers.