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

theorem Th22:
  for p being Point of Tunit_circle(2) holds Topen_unit_circle(p)
  = (Tunit_circle(2)) | (([#]Tunit_circle(2)) \ {p})
proof
  let p be Point of Tunit_circle(2);
  [#]Topen_unit_circle(p) = ([#]Tunit_circle(2)) \ {p} by Def10;
  hence thesis by PRE_TOPC:def 5;
end;
