
theorem Th24:
  for X be non empty set, Y be ComplexNormSpace holds
  C_NormSpace_of_BoundedFunctions(X,Y) is ComplexNormSpace
proof
  let X be non empty set;
  let Y be ComplexNormSpace;
  CLSStruct (# ComplexBoundedFunctions(X,Y), Zero_(ComplexBoundedFunctions
    (X,Y),ComplexVectSpace(X,Y)), Add_(ComplexBoundedFunctions(X,Y),
ComplexVectSpace(X,Y)), Mult_(ComplexBoundedFunctions(X,Y),ComplexVectSpace(X,Y
    )) #) is ComplexLinearSpace;
  hence thesis by Th23,CSSPACE3:2;
end;
