%% @texfile{
%%     filename="amsl-mch.tex",
%%     version="1.1",
%%     date="1-JUL-1991",
%%     filetype="AMS-LaTeX: documentation",
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%%     codetable="ISO/ASCII",
%%     checksumtype="line count",
%%     checksum="278",
%%     keywords="amslatex, ams-latex, tex",
%%     abstract="This file contains input for a sample monograph
%%            chapter illustrating the proper way to prepare such
%%            input for electronic submission to the AMS."
%%     }
%*********************************************************
%
% AMS-LaTeX 1.1 file for a sample monograph chapter for
% electronic submission.
%

\chapter[Sample \AMSLaTeX{} Monograph Chapter]%
{Sample \AMSLaTeX{} Electronic Manuscript\\
 for a Chapter of a Monograph,\\
 Matrix Algebras}

\section{Introduction}
This sample monograph illustrates the use of the \AMSLaTeX{} Version~1.1
book style.  This chapter is the output of the file {\bf amsl-mch.tex};
an author should use the coding in that file as a model.

In this sample chapter, brief instructions to authors are interspersed
with mathematical text extracted from (purposely unidentified)
published papers.  For instructions on preparing mathematical text,
the author is referred to {\it The Joy of \TeX}, by Michael Spivak
\cite{Spi}.  Detailed instructions for preparation of a monograph are
given in the {\bf Guidelines for Preparing Electronic Manuscripts}, to
which this sample chapter is one of several appendixes, and in
particular, in the section {\bf Monograph formatting}.

Additional sections illustrating the title page, table of contents,
and bibliography are also included in this sample monograph.

The bibliography was produced from the separate file {\bf amsl-mon.bbl},
which was, in turn, produced by \BibTeX{} from the file {\bf amsl-bib.bib}.
The same bibliographic file has been used (with a different \BibTeX{}
style) in the sample article which appears elsewhere in the
{\bf Guidelines} booklet.


\subsection{Monograph front matter}
The front matter of a monograph includes such elements as author
information, subject information, and an abstract.  This general
information is usually included in a separate file, for this example
{\bf amsl-mon.tex}, which also controls the compilation of the complete
monograph.  The tags are described in the {\bf Top matter} section of
the above-mentioned {\bf Guidelines}.

The table of contents was produced automatically by \LaTeX{} during
the compilation of the sample monograph; a second run was required to
get the correct page numbers (and other cross references) into the
{\bf .aux} file.


\subsection{Chapter top matter}
The chapter top matter comprises only the chapter title, including an
optional short form that will be used (if present) for running heads
and the table of contents.  See the first part of the sample file
{\bf amsl-mch.tex}, up to the first \verb|\section| instruction.


\subsection{Fonts}
The fonts used in this sample chapter are from the Computer Modern family;
they should be available to all authors preparing papers with these macros.
However, the final copy may be set by the AMS using other fonts.


\subsection{A mathematical extract}
The mathematical content of this sample chapter has been extracted from
published papers, with no effort made to retain any mathematical sense.
It is intended only to illustrate the recommended manner of input.

Mathematical symbols in text should always be input in math mode as
illustrated in the following paragraph.

A function is invertible in $C(X)$ if it is never zero, and in $C^*(X)$ if
it is bounded away from zero. In an arbitrary $A(X)$, of course, there
is no such description of invertibility which is independent of the 
structure of the algebra. Thus in \S 2 we associate to each noninvertible
$f\in A(X)$ a $z$-filter $\cal Z (f)$ that is a measure of where
$f$ is ``locally'' invertible in $A(X)$.

\section{Theorems, lemmas, and similar structures}
%
Theorems and lemmas and similar structures are all handled with
variations on the \verb|theorem| environment.  This is described in the
{\bf \AMSLaTeX{} User's Guide} [p.~32].

The lemma below uses the {\tt plain} theorem style and a heading at the
subsection level (section is the default, but a variation is used in
this sample monograph).

The lemma and proof illustrate the use of the \verb|enumerate|
environment to create lists.  The labels in these lists are not the
default ones (which would be (1), (2), etc.).  In the lemma, the
desired labels are entered using the optional \LaTeX{} bracket
notation; in the proof, the labels are generated automatically,
after invoking a command {\tt \char`\\alphenumi} that was defined
in the preamble of {\bf amsl-mon.tex} for that purpose.

Also in the proof, note the special handling of the
{\tt \char`\\qed}, which would ordinarily be set on a line
by itself, after the end of the {\tt enumerate} environment.

\begin{lem}
Let $f, g\in  A(X)$ and let $E$, $F$ be cozero
sets in $X$.
\begin{enumerate}
%  [want item labels of the form (a), (b), etc.]
\item[(a)] If $f$ is $E$-regular and $F\subseteq E$, then $f$ is $F$-regular.

\item[(b)] If $f$ is $E$-regular and $F$-regular, then $f$ is $E\cup F$-%
regular.
\end{enumerate}
\end{lem}

\begin{pf}
\begin{enumerate}
\alphenumi % Defined in the preamble of amsl-mon.tex
\item Obvious.

\item Let $h, k\in A(X)$ satisfy $hf|_E=1$ and $kf|_F=1$. Let
$w=h+k-fhk$. Then $fw|_{E\cup F}=1$.
\qed
\end{enumerate}
\renewcommand{\qed}{}
\end{pf}

\begin{defn}
For $f\in A(X)$, we define
\begin{equation}
\cal Z (f)=\{E\in Z[X]\: \text{$f$ is $E^c$-regular}\}.
\label{e:dispa}
\end{equation}
\end{defn}

\section{Roman type}
%
Numbers, punctuation, (parentheses), [brackets], $\{$braces$\}$, and
symbols used as tags should always be set in roman type.  The following
sample theorem illustrates how to code for roman type within the
statement of a theorem.

\begin{thm}
Let $\cal G$ be a free nilpotent-of-class-\rom{2} group of rank
$\ge 2$ with carrier $G$ and let
\begin{equation}
m : G\times G \to Z
\end{equation}
satisfy \rom{\eqref{e:dispau}}, \rom{\eqref{e:dispav}}, and
\rom{\eqref{e:dispax}}, and define $\kappa$ by
\rom{\eqref{e:dispaw}}.  Then this kappa-group is kappa-nilpotent
of class \rom{2} and kappa-metabelian, that is to say, it satisfies
\rom{S2} and \rom{S3}, but it is kappa-abelian if, and only if,
\begin{equation}
m(x,y) = -1\quad\text{for all $x, y \notin G'$}.
\label{e:dispba}
\end{equation}
\end{thm}

There are some other elements that should always be set in roman type.
Control sequences should be used for common mathematical functions and
operators like $\log$ and $\lim$ \cite[Chapter 14]{Spi}, and
\verb|\cite| should always be used when citing a reference.  Detailed
instructions are given in the {\bf Document body, roman type} section
in the above-mentioned {\bf Guidelines}.


\section{References}
%
Instructions for the input of references are given in the
{\bf Guidelines} mentioned above.  The bibliography of a monograph
is a separate chapter.  \BibTeX{} bibliographies always begin as
separate files.  The bibliography which follows this sample chapter
was produced from the file {\bf amsl-mon.bbl}.

The sample references have been chosen to illustrate the coding of the
most common types of references.  These references have been labeled
with ``key''-type labels, based on the author(s) name(s) and the year
of publication.  These labels were produced automatically by \BibTeX{}
using the style {\bf amsalpha.bst}; this \BibTeX{} style also sorts
the references into order by key.  The widest key is specified
automatically as the model from which the width of the left margin is
established.

Numbers may also be used as labels;
see the instructions in the {\bf Guidelines} and also the sample
article that accompanies them, where that style has been used.


\section{Figures}
%
Figures are handled as inserts, with an amount of space indicated that
should equal the exact height of the figure.  Extra space around the
figure will be provided automatically.  The positioning of figures may
need to be changed to obtain the best possible page layout.  Thus, it
is important to label your figures and use the labels in the text when
referring to them.  The figure caption should be positioned below
the figure.

Additional instructions for figures and other inserts, including
instructions for preparing art work, are given in the {\bf Guidelines}.
Note that the figures in this example are denoted ``a'' and ``b''.
This requires that the figure counter be adjusted so that it holds
the same value for both; to see how this is done, check the coding
in the input file.

\begin{exmp}
For the link in Figure \ref{f:afig}, the Massey product $\langle u_1,
u_2, u_3, u_4\rangle$ in $S^3-L$ is defined and consists of all
integer multiples of $\gamma_{1,4}$.  For the link in Figure \ref{f:bfig},
the Massey product $\langle u_1, u_2, u_3, u_4\rangle$ in $S^3-L$
contains the single element $\gamma_{1,4}$.  Since the links in
Figures \ref{f:afig} and \ref{f:bfig} are homotopic, the example
indicates that Massey products in $S^3-L$ with distinct $u_j$'s do not,
in general, determine homotopy invariants of the link.  For the link
in Figure \ref{f:afig} and the link in Figure \ref{f:bfig}, the Massey
product $\langle u_1, u_2, \dots, u_4\rangle$ in $\{S^3-L_i\}_{i=1}^4$
contains the single element $\gamma_{1,4}$.
\end{exmp}

%  art work measures 11.5pc for figure a, 7pc for figure b

\begin{figure}[t]
  \makeatletter
  \makeatother
  \renewcommand{\thefigure}{\arabic{figure}\rom{\subfig}}
  \vspace{11.5pc}
  \caption{}  % figure a
  \label{f:afig}
  \vspace{7pc}
  \renewcommand{\subfig}{b}
  \addtocounter{figure}{-1}
  \caption{}  % figure b
  \label{f:bfig}
\end{figure}

\section{Other headings}
%
\subsection{A subheading} % bold, run-in; do not type ending punctuation
We conclude by noting that another characterization of $A$-compactness
follows from Mandelker \cite{Mar}. We call a family $\cal S$ of closed sets in
$X\ A$-stable if every $f\in A(X)$ is bounded on some member of $\cal S$.
Then one can show (as in \cite{Mar}) that a space is $A$-compact if and only
if every $A$-stable family of closed sets with the finite intersection
property has nonempty intersection.

\subsubsection{A second-level subheading}
This paragraph is included only to illustrate the appearance of a
sub-subheading.

\endinput

% [end of file amsl-mch.tex]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
