 reserve x for set,
         n,m,k for Nat,
         r for Real,
         V for RealLinearSpace,
         v,u,w,t for VECTOR of V,
         Av for finite Subset of V,
         Affv for finite affinely-independent Subset of V;
reserve pn for Point of TOP-REAL n,
        An for Subset of TOP-REAL n,
        Affn for affinely-independent Subset of TOP-REAL n,
        Ak for Subset of TOP-REAL k;

theorem Th4:
  dim TOP-REAL n = n
proof
  the RLSStruct of TOP-REAL n=RealVectSpace Seg n by EUCLID:def 8;
  then (Omega).(TOP-REAL n)=RealVectSpace Seg n by RLSUB_1:def 4;
  then dim(Omega).(TOP-REAL n)=n by EUCLID_7:46;
  hence thesis by RLVECT_5:30;
end;
