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

theorem Th23:
  for p, q being Point of Tunit_circle(2) st p <> q holds q is
  Point of Topen_unit_circle(p)
proof
  let p, q be Point of Tunit_circle(2) such that
A1: p <> q;
  the carrier of Topen_unit_circle(p) = (the carrier of Tunit_circle(2)) \
  {p } by Def10;
  hence thesis by A1,ZFMISC_1:56;
end;
