--- a/text/appendixes/smallblobs.tex Thu Jun 24 10:17:19 2010 -0400
+++ b/text/appendixes/smallblobs.tex Thu Jun 24 14:20:38 2010 -0400
@@ -15,15 +15,9 @@
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
+This follows from Remark \ref{rem:for-small-blobs} 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}
-[...]
-}
-
\begin{proof}[Proof of Theorem \ref{thm:small-blobs}]
We begin by describing the homotopy inverse in small degrees, to illustrate the general technique.
--- a/text/evmap.tex Thu Jun 24 10:17:19 2010 -0400
+++ b/text/evmap.tex Thu Jun 24 14:20:38 2010 -0400
@@ -621,15 +621,16 @@
\nn{this should perhaps be a numbered remark, so we can cite it more easily}
-\begin{rem}
-For the proof of xxxx below we will need the following observation on the action constructed above.
+\begin{rem*}
+\label{rem:for-small-blobs}
+For the proof of Lemma \ref{lem:CH-small-blobs} 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 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}
+\end{rem*}