reserve x,y,z,X for set,
  T for Universe;

theorem Th29:
  for T being non empty TopSpace, p being Point of T, x being
Element of OpenNeighborhoods p ex W being Subset of T st W = x & p in W & W is
  open
proof
  let T be non empty TopSpace, p be Point of T, x be Element of
  OpenNeighborhoods p;
  set X = { V where V is Subset of T: p in V & V is open };
  x in the carrier of (InclPoset X)~;
  then x in the carrier of InclPoset X by Th3;
  hence thesis;
end;
