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Nov 19, 2013 at 21:21 comment added Vamsi Sorry. I was being silly.
Nov 19, 2013 at 21:21 vote accept Vamsi
Nov 19, 2013 at 21:16 comment added Misha @Vamsi: This is just a general nonsense from the point-set topology: If you have a sequence $z_n$ in a compact Hausdorff space $Z$ and every convergent subsequence in $(z_n)$ has the same limit $z$, then $\lim_n z_n=z$. In our setting the compact space is the space of K-qc maps normalized at 3 points.
Nov 19, 2013 at 20:41 history answered Misha CC BY-SA 3.0