  We examine Gromov's method of selecting a point "heavily covered" by
simplices formed by a given finite point sets, in order to understand the
dependence of the heavily covered point on parameters. We have no continuous
dependence, but manage to utilize the "homological continuous dependence" of
the heavily covered point. This allows us to infer some corollaries in a usual
way. We also give an elementary argument to prove the simplest of these
corollaries.
