reserve p,p1,p2,p3,q for Point of TOP-REAL 2;

theorem Th1:
  for P being compact non empty Subset of TOP-REAL 2 st P is
  being_simple_closed_curve holds W-min(P) in Lower_Arc(P) & E-max(P) in
  Lower_Arc(P) & W-min(P) in Upper_Arc(P) & E-max(P) in Upper_Arc(P)
proof
  let P be compact non empty Subset of TOP-REAL 2;
  assume P is being_simple_closed_curve;
  then
  Upper_Arc(P) is_an_arc_of W-min(P),E-max(P) & Lower_Arc(P) is_an_arc_of
  E-max(P),W-min(P) by JORDAN6:50;
  hence thesis by TOPREAL1:1;
end;
