  The class $\mathfrak C $ relative to countably compact topological spaces and
the class $\mathfrak P$ relative to pseudocompact spaces introduced by Z.
Frol\'ik are naturally generalized relative to every topological property. We
provide a characterization of such generalized Frol\'ik classes in the broad
case of properties defined in terms of filter convergence.
  If a class of spaces can be defined in terms of filter convergence, then the
same is true for its Frol\'ik class.
