CHARACTERIZATIONS OF CERTAIN CLASSES OF INFINITE-DIMENSIONAL METRIC SPACES

We characterize two classes of metric spaces as images under a closed, finite-to-one mapping of a zero-dimensional metric space. In the case of locally finite-dimensional spaces the mapping must be of strong local order, and for strongly countable-dimensional spaces the mapping must have weak local order. The results are analogues to characterizations by K. Morita (of finite-dimensional spaces) and J. Nagata (of countable-dimensional spaces).