 reserve
  S for non empty TopSpace,
  T for LinearTopSpace,
  X for non empty Subset of the carrier of S;

theorem Th4:
  for X be non empty TopSpace, S be non empty LinearTopSpace,
      f be Function of X,S,
      a be Real
  st f is continuous
    holds a(#)f is continuous
proof
  let X be non empty TopSpace, S be non empty LinearTopSpace,
      f be Function of X,S,
      a be Real;
  assume f is continuous; then
  for x being Point of X holds a(#)f is_continuous_at x by TMAP_1:44,Th2;
  hence thesis by TMAP_1:44;
end;
