--- a/text/appendixes/smallblobs.tex Mon Jun 21 15:28:02 2010 -0700
+++ b/text/appendixes/smallblobs.tex Tue Jun 22 18:05:09 2010 -0700
@@ -15,10 +15,14 @@
We can't quite do the same with all $\cV_k$ just equal to $\cU$, but we can get by if we give ourselves arbitrarily little room to maneuver, by making the blobs we act on slightly smaller.
\end{rem}
\begin{proof}
+This follows from the remark \nn{number it and cite it?} following the proof of
+Proposition \ref{CHprop}.
+\end{proof}
+\noop{
We choose yet another open cover, $\cW$, which so fine that the union (disjoint or not) of any one open set $V \in \cV$ with $k$ open sets $W_i \in \cW$ is contained in a disjoint union of open sets of $\cU$.
Now, in the proof of Proposition \ref{CHprop}
-\todo{I think I need to understand better that proof before I can write this!}
-\end{proof}
+[...]
+}
\begin{proof}[Proof of Theorem \ref{thm:small-blobs}]
--- a/text/evmap.tex Mon Jun 21 15:28:02 2010 -0700
+++ b/text/evmap.tex Tue Jun 22 18:05:09 2010 -0700
@@ -618,7 +618,6 @@
\end{proof}
-\noop{
\nn{this should perhaps be a numbered remark, so we can cite it more easily}
@@ -626,11 +625,13 @@
For the proof of xxxx below we will need the following observation on the action constructed above.
Let $b$ be a blob diagram and $p:P\times X\to X$ be a family of homeomorphisms.
Then we may choose $e$ such that $e(p\ot b)$ is a sum of generators, each
-of which has support arbitrarily close to $p(t,|b|)$ for some $t\in P$.
-This follows from the fact that the
-\nn{not correct, since there could also be small balls far from $|b|$}
+of which has support close to $p(t,|b|)$ for some $t\in P$.
+More precisely, the support of the generators is contained in a small neighborhood
+of $p(t,|b|)$ union some small balls.
+(Here ``small" is in terms of the metric on $X$ that we chose to construct $e$.)
\end{rem}
-}
+
+
\begin{prop}
The $CH_*(X, Y)$ actions defined above are associative.