reserve n for Element of NAT,
  i for Integer,
  a, b, r for Real,
  x for Point of TOP-REAL n;

theorem Th21:
  for p being Point of Tunit_circle(2) holds p is not Point of
  Topen_unit_circle(p)
proof
  let p be Point of Tunit_circle(2);
A1: p in {p} by TARSKI:def 1;
  the carrier of Topen_unit_circle(p) = (the carrier of Tunit_circle(2)) \
  {p} by Def10;
  hence thesis by A1,XBOOLE_0:def 5;
end;
