theorem Th39: :: C0SP3:39

for S being non empty compact TopSpace
for T being NormedLinearTopSpace
for a being Real
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
a * x = a * y