Topology Proceedings

Through basic properties relating to fragmentation, lower semicontinuity and evaluations along finite paths, we show a necessary and sufficient condition for the invariance 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 theorem to conditions of 0-dimensionality and of metrizability of the closure of the set of nontrivial fibers.