reserve
  X for non empty set,
  FX for Filter of X,
  SFX for Subset-Family of X;

theorem
  for T being non empty TopSpace,x being Point of T,
  F be Filter of the carrier of T holds x is_a_convergence_point_of F,T iff
  x is_a_convergence_point_of F2BOOL(F,T),T;
