equal
deleted
inserted
replaced
779 \end{figure} |
779 \end{figure} |
780 |
780 |
781 |
781 |
782 \begin{axiom}[Splittings] |
782 \begin{axiom}[Splittings] |
783 \label{axiom:vcones} |
783 \label{axiom:vcones} |
784 Let $c\in \cC_k(X)$ and |
784 Let $c\in \cC_k(X)$, with $0\le k < n$, and |
785 let $P$ be a finite poset of splittings of $c$. |
785 let $P$ be a finite poset of splittings of $c$. |
786 Then we can embed $\vcone(P)$ into the splittings of $c$, with $P$ corresponding to the base of $\vcone(P)$. |
786 Then we can embed $\vcone(P)$ into the splittings of $c$, with $P$ corresponding to the base of $\vcone(P)$. |
787 Furthermore, if $q$ is any decomposition of $X$, then we can take the vertex of $\vcone(P)$ to be $q$ up to a small perturbation. |
787 Furthermore, if $q$ is any decomposition of $X$, then we can take the vertex of $\vcone(P)$ to be $q$ up to a small perturbation. |
788 Also, any splitting of $\bd c$ can be extended to a splitting of $c$. |
788 Also, any splitting of $\bd c$ can be extended to a splitting of $c$. |
789 \end{axiom} |
789 \end{axiom} |