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;
