reserve T for TopStruct;
reserve GX for TopSpace;

theorem
  for A being Subset of T holds (A is open implies Cl([#](T) \ A) = [#](
T) \ A) & (T is TopSpace-like & Cl([#](T) \ A) = [#](T) \ A implies A is open)
proof
  let A be Subset of T;
  [#](T) \([#]T \ A) = A by Th3;
  then
A1: A is open iff [#]T \ A is closed;
  hence A is open implies Cl ([#]T \ A) = [#]T \ A by Th22;
  assume T is TopSpace-like & Cl([#]T \ A) = [#]T \ A;
  hence thesis by A1,Th22;
end;
