# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1317011482 21600
# Node ID 01c1daa7143734d9af70ff586b01800eb5c5fec4
# Parent  52e6b2d78dc43b621ba07e74663e321b48d2c3bb
remove TOP; searched of "topological" and "PL" to find places where we mention TOP

diff -r 52e6b2d78dc4 -r 01c1daa71437 text/appendixes/famodiff.tex
--- a/text/appendixes/famodiff.tex	Sun Sep 25 22:13:07 2011 -0600
+++ b/text/appendixes/famodiff.tex	Sun Sep 25 22:31:22 2011 -0600
@@ -49,9 +49,9 @@
 \end{enumerate}
 \end{lemma}
 
-Note: We will prove a version of item 4 of Lemma \ref{basic_adaptation_lemma} for topological
-homeomorphisms in Lemma \ref{basic_adaptation_lemma_2} below.
-Since the proof is rather different we segregate it to a separate lemma.
+%Note: We will prove a version of item 4 of Lemma \ref{basic_adaptation_lemma} for topological
+%homeomorphisms in Lemma \ref{basic_adaptation_lemma_2} below.
+%Since the proof is rather different we segregate it to a separate lemma.
 
 \begin{proof}
 Our homotopy will have the form
@@ -221,6 +221,8 @@
 
 % Edwards-Kirby: MR0283802
 
+\noop { %%%%%% begin \noop %%%%%%%%%%%%%%%%%%%%%%%
+
 The above proof doesn't work for homeomorphisms which are merely continuous.
 The $k=1$ case for plain, continuous homeomorphisms 
 is more or less equivalent to Corollary 1.3 of \cite{MR0283802}.
@@ -346,12 +348,12 @@
 
 \end{proof}
 
-
+} %%%%%% end \noop %%%%%%%%%%%%%%%%%%%
 
 \begin{lemma} \label{extension_lemma_c}
 Let $\cX_*$ be any of $C_*(\Maps(X \to T))$ or singular chains on the 
 subspace of $\Maps(X\to T)$ consisting of immersions, diffeomorphisms, 
-bi-Lipschitz homeomorphisms, PL homeomorphisms or plain old continuous homeomorphisms.
+bi-Lipschitz homeomorphisms, or PL homeomorphisms.
 Let $G_* \subset \cX_*$ denote the chains adapted to an open cover $\cU$
 of $X$.
 Then $G_*$ is a strong deformation retract of $\cX_*$.
@@ -359,7 +361,7 @@
 \begin{proof}
 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} (or \ref{basic_adaptation_lemma_2})
+This is exactly what Lemma \ref{basic_adaptation_lemma}
 gives us.
 More specifically, let $\bd P = \sum Q_i$, with each $Q_i\in G_{k-1}$.
 Let $F: I\times P\times X\to T$ be the homotopy constructed in Lemma \ref{basic_adaptation_lemma}.
diff -r 52e6b2d78dc4 -r 01c1daa71437 text/intro.tex
--- a/text/intro.tex	Sun Sep 25 22:13:07 2011 -0600
+++ b/text/intro.tex	Sun Sep 25 22:31:22 2011 -0600
@@ -541,7 +541,7 @@
 are equivalent to pivotal 2-categories, c.f. \S \ref{ssec:2-cats}.
 
 Finally, we need a general name for isomorphisms between balls, where the balls could be
-piecewise linear or smooth or topological or Spin or framed or etc., or some combination thereof.
+piecewise linear or smooth or Spin or framed or etc., or some combination thereof.
 We have chosen to use ``homeomorphism" for the appropriate sort of isomorphism, so the reader should
 keep in mind that ``homeomorphism" could mean PL homeomorphism or diffeomorphism (and so on)
 depending on context.
diff -r 52e6b2d78dc4 -r 01c1daa71437 text/ncat.tex
--- a/text/ncat.tex	Sun Sep 25 22:13:07 2011 -0600
+++ b/text/ncat.tex	Sun Sep 25 22:31:22 2011 -0600
@@ -84,7 +84,7 @@
 We are being deliberately vague about what flavor of $k$-balls
 we are considering.
 They could be unoriented or oriented or Spin or $\mbox{Pin}_\pm$.
-They could be topological or PL or smooth.
+They could be PL or smooth.
 %\nn{need to check whether this makes much difference}
 (If smooth, ``homeomorphism" should be read ``diffeomorphism", and we would need
 to be fussier about corners and boundaries.)
diff -r 52e6b2d78dc4 -r 01c1daa71437 text/tqftreview.tex
--- a/text/tqftreview.tex	Sun Sep 25 22:13:07 2011 -0600
+++ b/text/tqftreview.tex	Sun Sep 25 22:31:22 2011 -0600
@@ -42,7 +42,7 @@
 unoriented PL manifolds of dimension
 $k$ and morphisms homeomorphisms.
 (We could equally well work with a different category of manifolds ---
-oriented, topological, smooth, spin, etc. --- but for simplicity we
+oriented, smooth, spin, etc. --- but for simplicity we
 will stick with unoriented PL.)
 
 Fix a symmetric monoidal category $\cS$.