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391 \addtocounter{prop}{-2} |
391 \addtocounter{prop}{-2} |
392 |
392 |
393 These motivate the following definition. |
393 These motivate the following definition. |
394 |
394 |
395 \begin{defn} |
395 \begin{defn} |
396 A {\it local relation} is a collection subspaces $U(B; c) \sub \lf(B; c)$, |
396 A {\it local relation} is a collection of subspaces $U(B; c) \sub \lf(B; c)$, |
397 for all $n$-manifolds $B$ which are |
397 for all $n$-manifolds $B$ which are |
398 homeomorphic to the standard $n$-ball and all $c \in \cC(\bd B)$, |
398 homeomorphic to the standard $n$-ball and all $c \in \cC(\bd B)$, |
399 satisfying the following properties. |
399 satisfying the following properties. |
400 \begin{enumerate} |
400 \begin{enumerate} |
401 \item Functoriality: |
401 \item Functoriality: |