Proposition 4

Every projective linear variety of p dimensions in a projective space $P_n$ is closed in $P_n$ and homeomorphic to $P_p$; if $p < n$ its complement is dense in $P_n$.

!Diagram showing a hyperplane H in projective space P_n, with points x_0^{-1}x, x, and o, and another plane B.

Figure 4.

homogeneous coordinates satisfy a relation of the form $\sum_{i=0}^{n} a_i x_i = 0$, where the $a_i$ are not all zero (the "equation" of the hyperplane).