for S being non empty compact TopSpace
for T being NormedLinearTopSpace
for x being Point of (R_NormSpace_of_ContinuousFunctions (S,T))
for y being Point of (R_NormSpace_of_BoundedFunctions ( the carrier of S,T)) st x = y holds
||.x.|| = ||.y.|| by FUNCT_1:49;