Uniformly separating families of functions

A concept concerning separation of points by functions is defined and studied. This concept has close relations with superpositions of functions and dimension theory, and these relations are investigated. A theorem concerning the dimension of projections of Cantor manifolds inR ^m is proved. This is a part of the authors Ph.D thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor J. Lindenstrauss. The author wishes to thank Professor Lindenstrauss for his advice and encouragement during the preparation of this work.