@Klara: Sorry; that was supposed to be an $m$. No, each $y_k$ is simply in $\Bbb R$. But the point $y$ is in $B$ (why?) but not in $\Int\big((0,1)^\omega\big)$ (on account of $y_m$). — Brian M. Scott Mar 12 '13 at 14:05

I was deliberately being sketch-y so as not to take away all your fun. :) The idea is to form the quotient $(\Cpx^{n+1}\setminus\{0\})/\Intgr_{k}$, cover this quotient with the images of the sets $U_{\alpha}$, use the indicated functions as coordinates for the total space of some line bundle $L$, and observe that the transition functions are those for $\mathscr{O}(-k)$. — Andrew D. Hwang Nov 15 '15 at 12:40