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;
