
theorem Th7:
  for T being non empty TopStruct,
      s being sequence of T,
      x being Point of T holds
    x in Lim s
      iff
    for U1 being Subset of T st U1 is open & x in U1
    ex n being Nat st for m being Nat st n <= m holds s.m in U1
  proof
    let T be non empty TopStruct,s be sequence of T,
    x be Point of T;
    x in Lim s iff s is_convergent_to x by FRECHET:def 5;
    hence thesis;
  end;
