
theorem Th35:
  for X be non empty TopSpace holds
  R_Normed_Space_of_C_0_Functions(X) is RealNormSpace-like
proof
  let X be non empty TopSpace;
  for x, y being Point of R_Normed_Space_of_C_0_Functions(X)
  for a be Real holds ||.a*x.|| = |.a.| * ||.x.|| &
    ||.x+y.|| <= ||.x.|| + ||.y.|| by Th34;
  hence thesis by NORMSP_1:def 1;
end;
