%% @texfile{
%%     filename="amst-art.tex",
%%     version="2.1",
%%     date="30-JUL-1991",
%%     filetype="AMS-TeX: documentation",
%%     copyright="Copyright (C) American Mathematical Society,
%%            all rights reserved.  Copying of this file is
%%            authorized only if either:
%%            (1) you make absolutely no changes to your copy
%%                including name; OR
%%            (2) if you do make changes, you first rename it to some
%%                other name.",
%%     author="American Mathematical Society",
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%%            Technical Support Group,
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%%     telephone="401-455-4080 or (in the USA) 800-321-4AMS",
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%%     codetable="ISO/ASCII",
%%     checksumtype="line count",
%%     checksum="477",
%%     keywords="amstex, ams-tex, tex",
%%     abstract="This file contains input for a sample article
%%            illustrating the proper way to prepare such input
%%            for electronic submission to the AMS."
%%     }
%*********************************************************
%
% AMS-TeX 2.0+ file for a sample article for electronic submission.
%
\input amstex
\documentstyle{amsppt}
\NoBlackBoxes
%
%  Macros required to support the ability to process this file with
%  amsppt.sty 2.0 (these macros were not defined until amsppt.sty 2.1);
%  see Guidelines for Preparing Electronic Manuscripts (AMS-TeX).
%  Macro for roman text in non-roman environments.
\ifx\undefined\rom
  \define\rom#1{{\rm #1}}
\fi
%  Macro for current address.
\ifx\undefined\curraddr
  \def\curraddr#1\endcurraddr{\address {\it Current address\/}: #1\endaddress}
\fi

%  Macro for "cyrillic prime", transliteration of the Russian soft sign,
%  which appears in a bibliobraphy entry.
\def\cprime{$\mathsurround=0pt '$}

\topmatter
\title Sample \AmSTeX{} Electronic Manuscript for a Journal or Proceedings
 Article,\\
 On Maximal Ideals in Subalgebras of $C(X)$\endtitle
\rightheadtext{SAMPLE \AmSTeX{} ELECTRONIC ARTICLE}
\author Author One and Author Two\endauthor
\address Department of Mathematics, Northeastern University, Boston,
Massachusetts 02115\endaddress  %Research address for author one
\curraddr Department of Mathematics and Statistics, Case Western Reserve
University, Cleveland, Ohio 43403\endcurraddr %Current address for author one
\email XYZ\@Math.AMS.com\endemail
\address Mathematical Research Section, School of Mathematical Sciences,
Australian National University, Canberra ACT 2601, Australia %address for 
\email ABC\@mathsci.anu.edu.au\endemail %                     author two
\endaddress

\keywords Author's keywords go here\endkeywords
%  Math Subject Classifications 
\subjclass Primary 54C40, 14E20; Secondary 46E25, 20C20\endsubjclass
\abstract This paper is a sample prepared to illustrate for authors
the use of the \AmSTeX{} Version~2.0 preprint style.  An article of
this sort is suitable for publication in a journal or in a collection,
such as the proceedings of a conference.

The file used to prepare this sample is {\bf amst-art.tex}; an author
should use the coding in that file as a model.
\endabstract

%  \thanks will become a 1st page footnote.
%  Use \endgraf to indicate a new paragraph; a blank line or \par will
%  be recognized as an error.
%  Don't type a period at the end; it will be supplied.
\thanks The first author was supported in part by NSF
Grant \#000000.\endgraf
The final version of this paper will be submitted for
publication elsewhere\endthanks
\endtopmatter

\document

\head 1. Introduction                % bold, centered;
\endhead                             % don't type final punctuation
This sample paper illustrates the use of the \AmSTeX{} Version~2.0
preprint style.  In this sample paper, 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{25}.  Detailed instructions for preparation of
the structural elements of a paper are given in the {\bf Guidelines
for Preparing Electronic Manuscripts}, to which this sample paper is
one of several appendixes.

\subhead Top matter\endsubhead
The input format and content of the top matter can be best understood
by examining the first part of the sample file {\bf amst-art.tex}, up
through the {\tt\char`\\document} instruction.

The top matter includes both elements that must be input by the author
and a few that are provided automatically.  For details, see the
the {\bf Top matter} section in above-mentioned {\bf Guidelines}.

\subhead Fonts\endsubhead
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 AMS using other fonts.

\subhead A mathematical extract\endsubhead
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.

\head 2. Theorems, lemmas, and other proclamations\endhead
%
Theorems and lemmas are varieties of proclamations.  Either may have a
proof or a ``demonstration.''  The lemma and proof below illustrate
the use of a ``roster'' or itemized list; the first item in the proof
roster is run in.  Note that both proclamations and demonstrations
have their beginnings and ends marked in the file.

\proclaim{Lemma 1} Let $f, g\in  A(X)$ and let $E$, $F$ be cozero
sets in $X$.
\roster
\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.

\item"(c)" If $f(x)\ge c>0$ for all $x\in E$, then $f$ is $E$-regular.
\endroster
\endproclaim

\demo{Proof}
\roster\runinitem "(a)" Obvious.

\item"(b)" 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"(c)" Let $h=\max\{c,f\}$. Then $h|_E=f|_E$ and $h\ge c$. So $0<h^{-1}
\le c^{-1}$. Hence $h^{-1} \in C^*(X)\subseteq A(X)$, and 
$h^{-1} f|_E=1$. 
\endroster
\enddemo

\definition{Definition}
For $f\in A(X)$, we define
$$
\Cal Z (f)=\{E\in Z[X]\: \text{$f$ is $E^c$-regular}\}.
\tag 2.1
$$
\enddefinition

\head 3. Roman type\endhead
%
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.

\proclaim{3.1. Theorem}
Let $\Cal G$ be a free nilpotent-of-class-\rom{2} group of rank
$\ge 2$ with carrier $G$ and let
$$m : G\times G \to Z$$
satisfy \rom{(2.21)}, \rom{(2.22)}, and \rom{(2.24)}, and define
$\kappa$ by \rom{(2.23)}.  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,
$$m(x,y) = -1\quad\text{for all $x, y \notin G'$}.
\tag 3.1$$
\rom{(}Thus \rom{(3.1)} implies the trivial consequence
\rom{(2.1)}.\rom{)}  Assume now that \rom{(3.1)} does not hold,
so that the kappa-group is kappa-nonabelian.  Assume further that $m$
is not constant outside $G'$ \rom{(}inside $G'$ the values of $m$
clearly do not matter\rom{)}.  Then $\kappa$ is neither left nor right
linear, that is to say, neither \rom{S4} nor \rom{S5} holds:
\rom{I1} again holds, but none of \rom{I2--I5}.  As before,
\rom{I6} is equivalent to \rom{(2.25)}.  Now \rom{I7$'$}, however,
is equivalent to a condition similar to \rom{(2.25)}, namely
$$m(xz\sigma, yz\sigma) = m(x,y)\,.
\tag 3.2$$
\endproclaim

Other elements should always be set in roman type.  Control sequences
should be used for common mathematical functions and operators like
$\log$ and $\lim$ \cite{25\rm, Chapter 14}, and {\tt\char`\\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}.


\head 4. References\endhead
%
Detailed instructions for the input of references are given in the
{\bf Guidelines} mentioned above.

The references at the end of this sample file have been chosen to
illustrate the coding of the most common types of references.  The
sample references have been labeled with numbers, as {\tt\char`\\no 10},
etc.  It is also possible to use letters instead of numbers for
labels; see the instructions in the {\bf Guidelines} and also the
sample monograph chapter that accompanies them, where that style has
been used.


\head 5. Figures\endhead
%
Figures are handled as inserts, with an amount of space left 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}.

\example{Example 5}
For the link in Figure 5a, the Massey product $\langle u_1, u_2, u_3,
u_4, u_5\rangle$ in $S^3-L$ is defined and consists of all
integer multiples of $\gamma_{1,5}$.  For the link in Figure 5b,
the Massey product $\langle u_1, u_2, u_3, u_4, u_5\rangle$ in
$S^3-L$ contains the single element $\gamma_{1,5}$.  Since the links
in Figures 5a and 5b 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 5a
and the link in Figure 5b, the Massey product $\langle u_1, u_2, \dots,
u_5\rangle$ in $\{S^3-L_i\}_{i=1}^5$ contains the single element
$\gamma_{1,5}$.
\endexample

%  art work measures 11.5pc for figure 5a, 7pc for figure 5b

\topinsert
\vskip 11.5pc
\botcaption{Figure 5{\rm a}}\endcaption
\endinsert
\topinsert
\vskip 7pc
\botcaption{Figure 5{\rm b}}\endcaption
\endinsert

\head 6. Other headings\endhead
%
\subhead A subheading\endsubhead % bold, run-in; do not type ending punctuation
We conclude by noting that another characterization of $A$-com\-pact\-ness
follows from Mandelker \cite 5. 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 5) 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.

\subsubhead A second-level subheading\endsubsubhead
This paragraph is included only to illustrate the appearance of a
sub-subheading.

\subsubhead Comment on the authors' addresses\endsubsubhead
The addresses will be set in caps and small caps when the AMS prepares
final copy.  However, since authors may not have that font available in
the size required, ordinary roman type is substituted.

\Refs

\ref\no 1
\by     V. L. Arnol\cprime{}d, A. N. Varchenko, and S. M. Gusein-Zade
\book   Singularities of differentiable maps. \rom{I}
\publ   ``Nauka'' \publaddr Moscow \yr 1982 \lang Russian
\transl English transl. \publ Birkh\"auser \publaddr Basel \yr 1985
\endref
\ref\no 2 \bysame
\book   Singularities of differentiable maps. \rom{II}
\publ   ``Nauka'' \publaddr Moscow \yr 1984
\transl English transl. \publ Birkh\"auser \publaddr Basel \yr 1988
\endref
\ref\no 3
\by A. M. Arthurs
\book Complementary variational principles
\bookinfo 2nd ed. \publ Clarendon \publaddr Oxford\yr 1980
\endref
\ref\no 4
\by     H. Bass, E. H. Connell, and D. Wright
\paper  The Jacobian conjecture
\jour   Bull. Amer. Math. Soc.
\vol    7 \yr 1982 \pages 287--330
\endref
\ref\no 5
\by     H. Bass and G. H. Meisters
\paper  Polynomial flows in the plane
\jour   Adv. in Math. \vol 55 \yr 1985 \pages 173--203
\endref
\ref\no 6
\by     V. I. Berdichevski\u\i
\paper  A variational equation of continuum mechanics
\inbook Problems of the Mechanics of a Solid Deformable Body
\eds    L. I. Sedov and Yu. N. Robotnov
\nofrills\bookinfo (V. V. Novozhilov Sixtieth Birthday Vol.)
\publ   ``Sudostroenie''\publaddr Leningrad
\yr     1970 \pages 55--66\lang Russian
\endref
\ref\no 7
\by     B. Coomes
\book   Polynomial flows, symmetry groups, and conditions sufficient for 
        injectivity of maps
\bookinfo Ph.D. thesis, Univ. Nebraska--Lincoln
\yr     1988
\endref
\ref\no 8 \bysame % B. Coomes
\paper  The Lorenz system does not have a polynomial flow
\jour   J. Differential Equations
\toappear
\endref
\ref\no 9
\by     R. W. Cottle et al.\ (eds)
\book   Variational inequalities and complementarity problems
\bookinfo Proc. Internat. School (Erice, 1978)
\publ   Wiley \publaddr New York \yr 1980
\endref
\ref\no 10
\by     E. Formanek
\paper  Generating the ring of matrix invariants
\inbook Lecture Notes in Math. \vol 1197
\publ   Springer-Verlag \publaddr Berlin and New York
\yr     1986 \pages 73--82
\endref
\ref\no 11
\by     P. Gabriel
\paper  Unzerlegbare Darstellungen. \rom{II}
\jour   Manuscripta Math. \vol 6 \yr 1972 \pages 71--103
\endref
\ref\no 12
\by     J. Guckenheimer, P. Holmes, M. Martineau, and L. P. Robinson
\book   Nonlinear oscillations, dynamical systems, and bifurcations of vector
        fields
\publ   Springer-Verlag \publaddr New York
\yr     1983
\endref
\ref\no 13
\by     S. I. Hariharan and T. H. Moulton (eds.)
\book   Numerical methods for partial differential equations
\publ   Longman
\publaddr New York
\yr     1986
\endref
\ref\no 14
\by     J. K. Hunter and J. Scheurie
\paper  Perturbed solitary wave solutions of a model equation for water waves
\jour   Physica D 
\toappear
\endref
\ref\no 15
\by     P. D. Lax and C. D. Levermore
\paper  The small dispersion limit for the KdV equation. \rom{I}
\jour   Comm. Pure Appl. Math. 
\vol    36 \yr 1983 \pages 253--290
\nofrills\finalinfo (overview)
\moreref\paperinfo II
\jour   Comm. Pure Appl. Math. 
\vol    36 \yr 1983 \pages 571--594
\moreref\paperinfo III
\jour   Comm. Pure Appl. Math. 
\vol    36 \yr 1983 \pages 809--829
\endref
\ref\no 16
\by     J. L. Lions
\paper  Probl\`emes mixtes abstraits
\inbook Proc. Internat. Congr. Math. (Edinburgh, 1958)
\publ   Cambridge Univ. Press \publaddr London and New York \yr 1960
\pages  389--397
\endref
\ref\no 17
\by     A. E. Martynyuk
\paper  Some approximate methods for solving nonlinear equations with
  unbounded operators
\jour   Izv. Vyssh. Uchebn. Zaved. Mat. \vol 1966
\issue  6(55)\pages 85--94
\lang   Russian
\moreref \paperinfo addendum, ibid. \vol1967 \issue 8(63)\page 111
\endref
\ref\no 18
\by     G. H. Meisters
\paper  Jacobian problems in differential equations and algebraic geometry
\jour   Rocky Mountain J. Math. \vol 12 \yr 1982 \pages 679--705
\endref
\ref\no 19 \bysame  % Meisters
\paper  Polynomial flows on $\bold R^n$
\inbook Proc. Semester on Dynamical Systems (Warsaw, Autumn 1986)
\publ   Springer-Verlag
\publaddr Berlin, Heidelberg, and New York
\toappear
\endref
\ref\no 20
\by     G. H. Meisters and C. Olech
\paper  A poly-flow formulation of the Jacobian conjecture
\jour   Bull. Acad. Polon. Sci. S\'er. Sci. Math.
\vol    35
\yr     1987
\pages  725--731
\endref
\ref\no 21
\by     S. Osher
\paper  Shock capturing algorithms for equations of mixed type
\inbook Numerical Methods for Partial Differential Equations
\eds    S. I. Hariharan and T. H. Moulton
\publ   Longman \publaddr New York
\yr     1986
\pages  305--322
\endref
\ref\no 22
\by     L. A. Ostrovsky
\paper  Nonlinear internal waves in a rotating ocean
\paperinfo Part 2
\jour   Oceanology 
\vol    18
\yr     1978
\pages  181--191
\endref
\ref \no 23
\by     G. S. Petrov 
\paper  Elliptic integrals and their nonoscillatory behavior
\jour   Funktsional. Anal. i Pri\-lo\-zhen.
\vol    20
\yr     1986
\pages  46--49
\transl\nofrills English transl. in
\jour   Functional Anal. Appl. \vol 20 \yr 1986
\endref
\ref\no 24
\by     L. N. Slobodetski\u\i
\paper  Generalized Sobolev spaces and their application to boundary value
  problems for partial differential equations
\jour   Leningrad. Gos. Ped. Inst. Uchen. Zap.
\vol    197 \yr 1958 \pages 54--112
\lang   Russian
\transl\nofrills English transl. in
\jour   Amer. Math. Soc. Transl. (2) 
\vol 57 \yr 1966
\endref

\ref\no 25
\by     M. D. Spivak
\book   The joy of \TeX{}
\bookinfo 2nd revised ed.
\publ   Amer. Math. Soc., Providence, R.~I. \yr 1990\endref

\endRefs

\enddocument

% [end of file amst-art.tex]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
