reserve T for TopStruct;
reserve GX for TopSpace;
reserve T for TopStruct,
  x,y for Point of T;

theorem
  for S,T being TopSpace, f being Function of S,T, g being Function of
the TopStruct of S, the TopStruct of T st f = g holds f is continuous iff g is
  continuous
proof
  let S,T be TopSpace, f be Function of S,T, g be Function of the TopStruct of
  S, the TopStruct of T such that
A1: f = g;
  reconsider h = f as Function of S, the TopStruct of T;
  h is continuous iff g is continuous by A1,Th32;
  hence f is continuous iff g is continuous by Th33;
end;
