holds as a polynomial in variables .
and call it (the set of -valued points of) the projective space. The class of an element in is denoted by .
and call it (the set of -valued point of) the projective variety defined by .
That means, is divided into two pieces a nd .
That means, is covered by three ``open sets'' . Each of them is isomorphic to the plane (that is, the affine space of dimension 2).