reserve
  n, m for Nat,
  T for non empty TopSpace,
  M, M1, M2 for non empty MetrSpace;

theorem Th1:
  for A, B, S, T being TopSpace,
      f being Function of A,S, g being Function of B,T st
  the TopStruct of A = the TopStruct of B &
  the TopStruct of S = the TopStruct of T &
  f = g & f is open holds g is open
  proof
    let A, B, S, T be TopSpace;
    let f be Function of A,S;
    let g be Function of B,T;
    assume that
A1: the TopStruct of A = the TopStruct of B and
A2: the TopStruct of S = the TopStruct of T and
A3: f = g and
A4: f is open;
    let b be Subset of B;
    assume
A5: b is open;
    reconsider a = b as Subset of A by A1;
    a is open by A1,A5,TOPS_3:76;
    then f.:a is open by A4;
    hence thesis by A2,A3,TOPS_3:76;
  end;
