
theorem Th13:
  for S being non empty TopStruct for f being Collineation of S
  holds f" is Collineation of S
proof
  let S be non empty TopStruct;
  let f be Collineation of S;
A1: f" is bijective open by Def4;
A2: f is bijective by Def4;
  then
A3: rng f = [#]S by FUNCT_2:def 3;
  then f"" = f by A2,TOPS_2:51;
  then
A4: f"" is open by Def4;
  f"" is bijective by A2,A3,TOPS_2:51;
  hence thesis by A1,A4,Def4;
end;
