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

theorem Th33:
  for P being compact non empty Subset of TOP-REAL 2 st P={q where
q is Point of TOP-REAL 2: |.q.|=1} holds Upper_Arc(P) c= P & Lower_Arc(P) c= P
proof
  let P be compact non empty Subset of TOP-REAL 2;
  assume P={q where q is Point of TOP-REAL 2: |.q.|=1};
  then P is being_simple_closed_curve by JGRAPH_3:26;
  hence thesis by JORDAN6:61;
end;
