For every i,1≤i≤ n+1, let Ui be the subset of RPn=P(Rn+1) consisting of all points of homogeneous scoordinates (x1,...,xi,...,xn+1) such that xi=0.Show that Ui is an opens ubset of RPn. Show that...

For every i,1≤i≤ n+1, let Ui be the subset of RPn=P(Rn+1) consisting of all points of homogeneous scoordinates (x1,...,xi,...,xn+1) such that xi=0.Show that Ui is an opens ubset of RPn. Show that Ui∩Uj=/ 0f oralli, j. Show that there is a bijection between Ui and An defined such that

Whose inverse is the map

Does the above result extend to
  where K is any field?