reserve n   for Nat,
        r,s for Real,
        x,y for Element of REAL n,
        p,q for Point of TOP-REAL n,
        e   for Point of Euclid n;

theorem Th10:
  for O1 being Subset of TOP-REAL n, O2 being Subset of TopSpaceMetr Euclid n
  st O1 = O2 holds O1 is open iff O2 is open
  proof
    let O1 be Subset of TOP-REAL n,O2 be Subset of TopSpaceMetr Euclid n;
    assume
A1: O1 = O2;
    the TopStruct of TOP-REAL n = TopSpaceMetr Euclid n by EUCLID:def 8;
    hence thesis by A1;
  end;
