let X be non empty TopSpace; :: thesis: 0. (R_VectorSpace_of_C_0_Functions X) = X --> 0
A1: R_VectorSpace_of_C_0_Functions X is Subspace of RealVectSpace the carrier of X by RSSPACE:11;
0. (RealVectSpace the carrier of X) = X --> 0 ;
hence 0. (R_VectorSpace_of_C_0_Functions X) = X --> 0 by A1, RLSUB_1:11; :: thesis: verum