equal
deleted
inserted
replaced
818 |
818 |
819 \begin{proof} |
819 \begin{proof} |
820 After a small perturbation, we may assume that $q$ is simultaneously transverse to all the splittings in $P$, and |
820 After a small perturbation, we may assume that $q$ is simultaneously transverse to all the splittings in $P$, and |
821 (by Axiom \ref{axiom:splittings}) that $c$ splits along $q$. |
821 (by Axiom \ref{axiom:splittings}) that $c$ splits along $q$. |
822 We can now choose, for each splitting $p$ in $P$, a common refinement $p'$ of $p$ and $q$. |
822 We can now choose, for each splitting $p$ in $P$, a common refinement $p'$ of $p$ and $q$. |
823 This constitutes the middle part of $\vcone(P)$. |
823 This constitutes the middle part ($P\times \{0\}$ above) of $\vcone(P)$. |
824 \end{proof} |
824 \end{proof} |
825 |
825 |
826 |
826 |
827 \noop{ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
827 \noop{ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
828 |
828 |