
theorem Th11:
  for X be non empty set, Y be ComplexNormSpace holds 0.
  C_VectorSpace_of_BoundedFunctions(X,Y) = (X -->0.Y)
proof
  let X be non empty set;
  let Y be ComplexNormSpace;
  C_VectorSpace_of_BoundedFunctions(X,Y) is Subspace of ComplexVectSpace(
  X,Y) & 0.ComplexVectSpace(X,Y) = (X -->0.Y) by Th7,CSSPACE:11,LOPBAN_1:def 3;
  hence thesis by CLVECT_1:30;
end;
