
theorem Th5:
  for X being TopStruct, Y,Z being non empty TopStruct,f being
  Function of X,Y, h being Function of Y,Z st h is being_homeomorphism & f is
  continuous holds h*f is continuous
proof
  let X be TopStruct,Y,Z be non empty TopStruct,f be Function of X,Y, h be
  Function of Y,Z;
  assume that
A1: h is being_homeomorphism and
A2: f is continuous;
  h is continuous by A1,TOPS_2:def 5;
  hence thesis by A2,TOPS_2:46;
end;
