A note on simplification of z-ordinal sum construction.

We study the properties of z -ordinal sum construction and show that it can always be expressed in the reduced basic form. This means that it is enough to assume only trivial semigroups in the branching set and we can always remove semigroups with duplicate carriers. We also investigate the cardinality of the minimal branching set corresponding to monotone (and non-monotone) functions defined on the unit interval constructed via z -ordinal sum construction. [ABSTRACT FROM AUTHOR]