reserve T for TopStruct;
reserve GX for TopSpace;
reserve T for TopStruct,
  x,y for Point of T;

theorem
  for T being TopSpace, X being set holds X is open Subset of T iff X is
  open Subset of the TopStruct of T
proof
  let T be TopSpace, X be set;
  X in the topology of T iff X in the topology of the TopStruct of T;
  hence thesis by Def2;
end;
