  The paper studies complementary choice functions, i.e. monotonic and
consistent choice functions. Such choice functions were introduced and used in
the work \cite{RY} for investigation of matchings with complementary contracts.
Three (universal) ways of constructing such functions are given: through
pre-topologies, as direct images of completely complementary (or pre-ordered)
choice functions, and with the help of supermodular set-functions.
