reserve k,j,n for Nat,
  r for Real;
reserve x,x1,x2,y for Element of REAL n;
reserve f for real-valued FinSequence;
reserve p,p1,p2,p3 for Point of TOP-REAL n,
  x,x1,x2,y,y1,y2 for Real;
reserve p,p1,p2 for Point of TOP-REAL 2;

theorem Th39:
  the carrier of Euclid n = the carrier of TOP-REAL n
proof
  thus the carrier of Euclid n = the carrier of TopSpaceMetr Euclid n
    .= the carrier of the TopStruct of TOP-REAL n by Def8
    .= the carrier of TOP-REAL n;
end;
