  Two simple predicates are adopted and certain real-valued piecewise
continuous functions are constructed from them. This type of maps will be
called quasi-step maps and aim to separate the fixed points of an iteration map
in an interval. The main properties of these maps are studied. Several worked
examples are given where appropriate quasi-step maps for Newton and Halley
iteration maps illustrate the main features of quasi-step maps as tools for
global separation of roots.
