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% LaTeX sample file for TMNA volumes.
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\documentclass{tmna}
% The following items give publication information for the TMNA logo
\begin{document}
\title[Maximal Ideals in Subalgebras of $C(X)$]{Sample Paper for TMNA\\
On Maximal Ideals in Subalgebras of $C(X)$}
\author[Author One --- Author Two]{Author One --- Author Two}
\address
{\textsc{Author One}\\
Department of Mathematics\\
Northeastern University\\
Boston, MA 02115, USA}
\email{xyz@math.ams.org}
\address{\textsc{Author Two}\\
Mathematical Research Section\\
School of Mathematical Sciences\\
Australian National University\\
Canberra ACT 2601, AUSTRALIA}
%\submittedby {}
%\dedicatory {This is dedicated to ....}
% Math Subject Classifications
\subjclass[2010] {Primary: 54C40, 14E20; Secondary: 46E25, 20C20}
\keywords{Keyword1; keyword2; keywordx}
\thanks{The final version of this paper will be submitted for
publication elsewhere.}
\thanks{The first author was supported in part by NSF
Grant \#000000.}
\begin{abstract}%
In this paper we present the fundamental result of the fundamental theory.
\end{abstract}
\maketitle
\section{Introduction} % don't type final punctuation
This sample paper illustrates the use of the AMSART
document class version~2.20.1 with additional macros and modifications
for the journal {\it Topological Methods in
Nonlinear Analysis}. In this sample paper brief instructions to authors will
be 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}, second edition, by Michael Spivak
\cite{spivak:jot} and {\it \LaTeX}: {\it A Document Preparation System} by
Leslie Lamport \cite{lamport:latex}.
\subsection{Top matter} % do not type ending punctuation
The input format and content of the top matter can be best understood
by examining the first part of the sample file {\bf TMNA-L.tex}, up
through the \verb+\begin{document}+ instruction.
The top matter includes both elements that must be input by the author and a
few that are provided automatically. The author names and the title that are
to appear in the running heads should be input between square brackets as an
option to the \verb+\author+ and \verb+\title+ commands, respectively. The full
names and title should be used unless they require too much space; in that
event, abbreviated forms should be substituted. In the top matter, the title is
input in caps and lowercase and will be set in all caps. The author names
should be input in caps and lowercase; they will automatically be set in
caps/small caps.
For each author an address should be input. The author's name should be input
in upper and lowercase with a call to small caps
%%% GM:
({\tt \string\textsc\{Author's Name\}} or
{\tt\{\char`\\sc Author's Name\}}) preceding
the text. The rest of the address information will default to roman type. The
complete addresses for each author should be entered in the order that names
appear on the title page. Addresses are considered part of the top matter but
are set at the end of the paper following the references.
If an author's current address is different from the address where the research
was carried out, then both addresses should be given with the current address
second and coded as indicated in this sample file. Following these addresses,
an electronic mail address should be given, if one exists.
Subject classifications ({\tt\char`\\subjclass}) and acknowledgments
({\tt\char`\\thanks}) are part of the top matter and will appear as unmarked
footnotes at the bottom of the first page. Subject classifications
({\tt\char`\\subjclass}) are required. Use the 1991 Mathematics Subject
Classification that appears in annual indexes of {\it Mathematical Reviews\/}
beginning in 1990. (The two-digit code from the Contents is not sufficient.)
Use {\tt\char`\\thanks} for the footnotes that appear on the first page
concerning any specific information the author wishes to convey. Refer to the
example in this sample paper.
\subsection{Fonts}
The fonts used in this paper 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 publisher using other fonts.
\subsection{A mathematical extract}
The mathematical content of this sample paper 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 $A(X)$. This correspondence extends to
one between maximal ideals of $A(X)$ and $z$-ultrafilters on $X$.
In \S 3 we use the filters $\Cal Z (f)$ to describe the intersection of
the free maximal ideals in any algebra $A(X)$. Finally, our main result
allows us to introduce the notion of $A(X)$-compactness, of which
compactness and realcompactness are special cases. In \S 4 we show how
the Banach-Stone theorem extends to $A(X)$-compact spaces.
\section{Theorems, lemmas, and other proclamations}
Theorems and lemmas are varieties of \verb+theorem+ environments. In this
document, a \verb+theorem+ environment called \verb+lemma+ has been created,
which is used below. Also, there is a proof, which is in the predefined
\verb+pf+ environment. The lemma and proof below illustrate the use of
the \verb+enumerate+ environment.
\begin{lemma}
Let $f, g\in A(X)$, and let $E$, $F$ be cozero
sets in $X$.
\begin{enumerate}
\item If $f$ is $E$-regular and $F\subseteq E$, then $f$ is $F$-regular.
\item If $f$ is $E$-regular and $F$-regular, then $f$ is $E\cup F$-%
regular.
\item If $f(x)\ge c>0$ for all $x\in E$, then $f$ is $E$-regular.
\end{enumerate}
\end{lemma}
\begin{proof}
\begin{enumerate}
\item Obvious.
\item Let $h, k\in A(X)$ satisfy $hf|_E=1$, and $kf|_F=1$. Let
$w=h+k-fhk$. Then $fw|_{E\cup F}=1$.
\item Let $h=\max\{c,f\}$. Then $h|_E=f|_E$, and $h\ge c$. So $0