Several classes of generalized inverses of a given m X n matrix are considered. A co ll ection of continuous maps is given, each of which maps a class of generalized inverses onto a stronge r c lass and the elements of the stronger class are the fixed points of the map. For the case of EPr matrices one of these maps is studied in more detail. The various classes of generalized inverses are characterized as subspaces of the space of all n X m matrices.