
theorem Th41:
  for X being non empty TopSpace holds
  CLSStruct (# CC_0_Functions X,
    Zero_(CC_0_Functions X, ComplexVectSpace(the carrier of X)),
    Add_(CC_0_Functions X, ComplexVectSpace(the carrier of X)),
    Mult_(CC_0_Functions X, ComplexVectSpace(the carrier of X)) #)
      is Subspace of ComplexVectSpace(the carrier of X) by Th40;
