 reserve
  S for non empty TopSpace,
  T for LinearTopSpace,
  X for non empty Subset of the carrier of S;

theorem
for S be non empty TopSpace, T be non empty LinearTopSpace
  holds RLSStruct
(# ContinuousFunctions(S,T),
Zero_(ContinuousFunctions(S,T),RealVectSpace(the carrier of S,T)),
Add_(ContinuousFunctions(S,T),RealVectSpace(the carrier of S,T)),
Mult_(ContinuousFunctions(S,T), RealVectSpace(the carrier of S,T))
#) is Subspace of RealVectSpace(the carrier of S,T) by Th5,RSSPACE:11;
