--- a/text/appendixes/famodiff.tex	Thu May 27 17:39:11 2010 -0700
+++ b/text/appendixes/famodiff.tex	Thu May 27 17:52:46 2010 -0700
@@ -9,7 +9,7 @@
 (That is, $r_\alpha : X \to [0,1]$; $r_\alpha(x) = 0$ if $x\notin U_\alpha$;
 for fixed $x$, $r_\alpha(x) \ne 0$ for only finitely many $\alpha$; and $\sum_\alpha r_\alpha = 1$.)
 Since $X$ is compact, we will further assume that $r_\alpha = 0$ (globally) 
-for all but finitely many $\alpha$. \nn{Can't we just assume $\cU$ is finite? Is something subtler happening? -S}
+for all but finitely many $\alpha$.
 
 Consider  $C_*(\Maps(X\to T))$, the singular chains on the space of continuous maps from $X$ to $T$.
 $C_k(\Maps(X \to T))$ is generated by continuous maps
@@ -214,7 +214,7 @@
 Then $G_*$ is a strong deformation retract of $\cX_*$.
 \end{lemma}
 \begin{proof}
-If suffices to show that given a generator $f:P\times X\to T$ of $\cX_k$ with
+It suffices to show that given a generator $f:P\times X\to T$ of $\cX_k$ with
 $\bd f \in G_{k-1}$ there exists $h\in \cX_{k+1}$ with $\bd h = f + g$ and $g \in G_k$.
 This is exactly what Lemma \ref{basic_adaptation_lemma}
 gives us.