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

theorem Th40:
  for S be non empty compact TopSpace,T be NormedLinearTopSpace holds
  (the carrier of S) --> 0.T = 0.R_NormSpace_of_ContinuousFunctions(S,T)
proof
  let S be non empty compact TopSpace,T be NormedLinearTopSpace;
  (the carrier of S)-->0.T = 0.R_VectorSpace_of_ContinuousFunctions(S,T)
    by Th9;
  hence thesis;
end;
