equal
deleted
inserted
replaced
535 \end{axiom} |
535 \end{axiom} |
536 |
536 |
537 This axiom needs to be strengthened to force product morphisms to act as the identity. |
537 This axiom needs to be strengthened to force product morphisms to act as the identity. |
538 Let $X$ be an $n$-ball and $Y\sub\bd X$ be an $n{-}1$-ball. |
538 Let $X$ be an $n$-ball and $Y\sub\bd X$ be an $n{-}1$-ball. |
539 Let $J$ be a 1-ball (interval). |
539 Let $J$ be a 1-ball (interval). |
540 We have a collaring homeomorphism $s_{Y,J}: X\cup_Y (Y\times J) \to X$. |
540 Let $s_{Y,J}: X\cup_Y (Y\times J) \to X$ be a collaring homeomorphism |
541 (Here we use $Y\times J$ with boundary entirely pinched.) |
541 (see the end of \S\ref{ss:syst-o-fields}). |
|
542 Here we use $Y\times J$ with boundary entirely pinched. |
542 We define a map |
543 We define a map |
543 \begin{eqnarray*} |
544 \begin{eqnarray*} |
544 \psi_{Y,J}: \cC(X) &\to& \cC(X) \\ |
545 \psi_{Y,J}: \cC(X) &\to& \cC(X) \\ |
545 a & \mapsto & s_{Y,J}(a \cup ((a|_Y)\times J)) . |
546 a & \mapsto & s_{Y,J}(a \cup ((a|_Y)\times J)) . |
546 \end{eqnarray*} |
547 \end{eqnarray*} |