--- a/text/evmap.tex	Wed Sep 15 13:33:14 2010 -0500
+++ b/text/evmap.tex	Wed Sep 15 13:33:40 2010 -0500
@@ -26,7 +26,7 @@
 sort-of-simplicial set into a sort-of-simplicial space.
 Taking singular chains of this space we get $\btc_*(X)$.
 The details are in \S \ref{ss:alt-def}.
-We also prove a useful lemma (\ref{small-blobs-b}) which says that we can assume that
+We also prove a useful result (Lemma \ref{small-blobs-b}) which says that we can assume that
 blobs are small with respect to any fixed open cover.
 
 
@@ -226,9 +226,9 @@
 \end{itemize}
 
 We can summarize the above by saying that in the typical continuous family
-$P\to \BD_k(M)$, $p\mapsto (B_i(p), u_i(p), r(p)$, $B_i(p)$ and $r(p)$ are induced by a map
+$P\to \BD_k(M)$, $p\mapsto \left(B_i(p), u_i(p), r(p)\right)$, $B_i(p)$ and $r(p)$ are induced by a map
 $P\to \Homeo(M)$, with the twig blob labels $u_i(p)$ varying independently.
-We note that while have no need to allow the blobs $B_i(p)$ to vary independently of the field $r(p)$,
+We note that while we've decided not to allow the blobs $B_i(p)$ to vary independently of the field $r(p)$,
 if we did allow this it would not affect the truth of the claims we make below.
 In particular, we would get a homotopy equivalent complex $\btc_*(M)$.