Solotion let p: rn+1∖{0}→rk+1∖{0} be a smooth function, and suppose that for some d∈z, p(λx)=λdp(x) for all λ∈r∖{0} and x∈rn+1∖{0}. (such a function is said to be homogeneous of degree d.) show that the map p~: rpn→rpk defined by p~([x])=[p(x)] is well defined and smooth.