%----------------------------------------------------------------------------- % Beginning of CONM-M.let-e %----------------------------------------------------------------------------- Following this letter are three files (CONM-M.STY, CONM-M.TEX, CONM-MREFS.TEX and CONM-M.CHECKLIST) to be used when preparing a monograph in AMS-TeX 2.1, for a volume in the Contemporary Mathematics series. To make it easier to load these files separately on your system, they are separated by file delimiters. The .STY file is used to modify the AMS-TeX preprint style to the CONM-M style. Instructions for using this file are listed at the top. The CONM-M.TEX file is a sample of the macros defined in the .STY file. Before preparing your paper you should TeX this file and print it to test the macros and to get instructions for their use. The CONM-MREFS.TEX file is a supplemental file that illustrates how references should be typed; it too should be TeXed and printed. The .CHECKLIST file should be printed and used to help you avoid the most common problems. Once your paper has been accepted for publication in CONM-M, please send all the necessary .TEX files to our Internet address: PUB-SUBMIT@MATH.AMS.COM. When you send the file please be sure to include a message that identifies both the publication series and the editor of the volume. Should you have any technical questions, please contact our Technical Support Group at 800-321-4AMS or 401-455-4080. They can also be reached through electronic mail at Internet: tech-support@math.ams.com. %----------------------------------------------------------------------------- % End of CONM-M.let-e %----------------------------------------------------------------------------- %----------------------------------------------------------------------------- % Beginning of conm-m.sty %----------------------------------------------------------------------------- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This file is designed to work with AMS-TeX version 2.1. % % The TeX code defined here will modify the AMS-TeX 2.1 preprint style to % the CONM-M style. It sets up the correct page size, % puts a logo and a copyrightline on the first page, and formats the % top matter, headings and references appropriately. % % % Instructions: % % 1. Create a file named conm-m.sty containing the data in the lines % from %%% conm-m.sty %%% through \endinput . Install the file % in the same directory as amsppt.sty . % % 2. In a data file, include the line, \documentstyle{conm-m} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % First input the preprint style \def\next{AMSPPT}\ifx\styname\next \else\input amsppt.sty\fi \catcode`\@=11 % Set the page size and first-page sink appropriately \pageheight{47pc} \pagewidth{29pc} \parindent=12\p@ % Page numbers and running heads are provided by default, as defined % in AMSPPT.STY. Headline text is centered, and page numbers are % positioned at the outside corners. To suppress page numbers and/or % running heads, include \NoPageNumbers and/or \NoRunningHeads in the % input file, as appropriate. % In CONM-M, we do want running heads. We must provide suitable % fonts definitions. CONM-M specs call for 7-point headlines, % but \sevenpoint is not defined in AMSPPT.STY; substitute \eightpoint, % which is defined. \def\foliofont@{\eightrm} \def\headlinefont@{\eightpoint} % text font is 10-on-13; AMSPPT.STY is 10-on-12 \addto\tenpoint{\normalbaselineskip13\p@ \abovedisplayskip6\p@ plus6\p@ minus0\p@ \belowdisplayskip6\p@ plus6\p@ minus0\p@ \abovedisplayshortskip0\p@ plus3\p@ minus0\p@ \belowdisplayshortskip2\p@ plus3\p@ minus0\p@ \ifsyntax@ \else \setbox\strutbox\hbox{\vrule height9\p@ depth4\p@ width\z@}% \setbox\strutbox@\hbox{\vrule height8\p@ depth3\p@ width\z@}% \fi \normalbaselines\rm} % modify \title to use a larger font \font@\titlebf=cmbx10 scaled \magstep2 \font@\titlei=cmmi10 scaled \magstep2 \font@\titlesy=cmsy10 scaled \magstep2 \def\titlefont{\normalbaselineskip18\p@ \textonlyfont@\bf\titlebf \ifsyntax@\else \textfont\z@\titlebf \scriptfont\z@\tenrm \scriptscriptfont\z@\sevenrm \textfont\@ne\titlei \scriptfont\@ne\teni \scriptscriptfont\@ne\seveni \textfont\tw@\titlesy \scriptfont\tw@\tensy \scriptscriptfont\tw@\sevensy \textfont\thr@@\tenex \scriptfont\thr@@\tenex \scriptscriptfont\thr@@\tenex \fi \normalbaselines\titlebf} \def\title#1\endtitle{\global\setbox\titlebox@ \vtop{\titlefont\bf \raggedcenter@ \baselineskip18pt #1\endgraf}% \ifmonograph@ \edef\next{\the\leftheadtoks}% \ifx\next\empty \leftheadtext{#1}\fi \fi \edef\next{\the\rightheadtoks}\ifx\next\empty \rightheadtext{#1}\fi } % chapter heading in ten point \def\romanchapternum{\gdef\chapterno@{\uppercase\expandafter{\romannumeral \chaptercount@}}} \def\chapterno@{\the\chaptercount@} \def\chapter{\let\savedef@\chapter \def\chapter##1{\let\chapter\savedef@ \leavevmode\hskip-\leftskip \rlap{\vbox to\z@{\vss\centerline{\tenpoint \frills@{CHAPTER\space\afterassignment\chapterno@\global\chaptercount@=}% ##1\unskip}\baselineskip34pt\null}}\hskip\leftskip}% \nofrillscheck\chapter} % authors are set in all caps \def\author{\let\savedef@\author \def\author##1\endauthor{\global\setbox\authorbox@ \vbox{\tenpoint\raggedcenter@ \frills@\uppercasetext@{\ignorespaces##1}\endgraf} \edef\next{\the\leftheadtoks}% \ifx\next\empty\expandafter\uppercase{\leftheadtext{##1}}\fi} \nofrillscheck\author} % \abstract differs from the one in AMSPPT.STY by the use of a slightly % larger indentation. \def\abstract{\let\savedef@\abstract \def\abstract{\let\abstract\savedef@ \setbox\abstractbox@\vbox\bgroup\noindent$$\vbox\bgroup\indenti=3pc \def\envir@end{\endabstract}\advance\hsize-2\indenti \def\usualspace{\enspace}\eightpoint \noindent \frills@{{\smc Abstract.\enspace}}}% \nofrillscheck\abstract} % change default first page sink \outer\def\endtopmatter{\add@missing\endabstract \edef\next{\the\leftheadtoks}\ifx\next\empty \expandafter\leftheadtext\expandafter{\the\rightheadtoks}\fi \ifmonograph@\else \ifx\thesubjclass@\empty\else \makefootnote@{}{\thesubjclass@}\fi \ifx\thekeywords@\empty\else \makefootnote@{}{\thekeywords@}\fi \ifx\thethanks@\empty\else \makefootnote@{}{\thethanks@}\fi \fi \pretitle \begingroup % to localize variant topskip \ifmonograph@\topskip9pc \else \topskip4pc \fi \box\titlebox@ \endgroup \preauthor \ifvoid\authorbox@\else \vskip2.5pcplus1pc\unvbox\authorbox@\fi \preaffil \ifvoid\affilbox@\else \vskip1pcplus.5pc\unvbox\affilbox@\fi \predate \ifx\thedate@\empty\else \vskip1pcplus.5pc\line{\hfil\thedate@\hfil}\fi \preabstract \ifvoid\abstractbox@\else \vskip1.5pcplus.5pc\unvbox\abstractbox@ \fi \ifvoid\tocbox@\else\vskip1.5pcplus.5pc\unvbox\tocbox@\fi \prepaper \vskip2pcplus1pc\relax } % Heading styles are different from AMSPPT.STY: % \heading is bold, otherwise the same. % \subheading and \subsubheading are indented, otherwise the same. \def\headfont@{\bf} \def\refheadfont@{\smc} \let\varindent@\indent % Indentation for \proclaim, \demo, etc., are the same as for \subhead, % and are taken care of by \varindent. % \proclaim head font is small caps, and the text font is italic (not \sl). % \demo is preceded by a \smallskip and followed by none (not \medskip). \def\proclaimheadfont@{\smc} \let\proclaim\relax \outer\def\proclaim{% \let\savedef@\proclaim \let\proclaim\relax \add@missing\endroster \add@missing\enddefinition \add@missing\endproclaim \envir@stack\endproclaim \def\proclaim##1{\restoredef@\proclaim \penaltyandskip@{-100}\medskipamount\varindent@ \def\usualspace{{\proclaimheadfont@\enspace}}\proclaimheadfont@ \ignorespaces##1\unskip\frills@{.\enspace}% \it\ignorespaces}% After printing the name of the theorem, switch to \sl. \nofrillscheck\proclaim} \def\remark{\let\savedef@\remark \let\remark\relax \add@missing\endroster \add@missing\endproclaim \envir@stack\endremark \def\remark##1{\restoredef@\remark \penaltyandskip@\z@\smallskipamount {\def\usualspace{{\remarkheadfont@\enspace}}% \varindent@\remarkheadfont@\ignorespaces##1\unskip\frills@{.\enspace}}\rm \ignorespaces}\nofrillscheck\remark} \def\remarkheadfont@{\smc} \def\enddemo{\par\revert@envir\enddemo \endremark\vskip\z@ plus 1\p@ minus 0\p@} % \Refs differs only in the skip below, which is 8pt (default=6pt) % Before reiterating definition only for that, check to see if it matters. \def\citefont@{\bf} \def\refsfont@{\tenpoint} \let\Refs\relax \outer\def\Refs{\add@missing\endroster \add@missing\endproclaim \let\savedef@\Refs \let\Refs\relax % because of \outer-ness \def\Refs##1{\restoredef@\Refs \if\notempty{##1}\penaltyandskip@{-200}\aboveheadskip \begingroup \raggedcenter@\refheadfont@ \ignorespaces##1\endgraf\endgroup \penaltyandskip@\@M\belowheadskip \fi \begingroup\def\envir@end{\endRefs}\refsfont@\sfcode`\.\@m }% \nofrillscheck{\csname Refs\expandafter\endcsname\frills@{{References}}}} \def\logo@{} %\baselineskip2pc \hbox to\hsize{\hfil\eightpoint Typeset by \AmSTeX}} \catcode`\@=13 \Monograph \def\amsversion{2.1} \endinput %----------------------------------------------------------------------------- % End of conm-m.sty %----------------------------------------------------------------------------- %----------------------------------------------------------------------------- % Beginning of conm-m.tex %----------------------------------------------------------------------------- % % AMS-TeX 2.1 sample file for CONM-M volumes. % \input amstex \documentstyle{conm-m} \NoBlackBoxes % \topmatter \title\chapter{1} Sample Paper for CONM-M,\\ On Maximal Ideals in Subalgebras of $C(X)$\endtitle \endtopmatter \leftheadtext{1. Sample Paper for CONM-M} \document \head 1. Introduction % bold, centered; \endhead % don't type final punctuation This sample paper illustrates the use of the \AmSTeX{} Version~2.1 preprint style with additional macros for the series {\it Contemporary Mathematics}. 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{12}. \subhead 1.1. Top matter\endsubhead The input format and content of the top matter for a monograph consists only of the chapter title as illustrated in this sample file {\bf CONM-M.tex}. If it is desired to have chapter numbers be uppercase Roman numerals rather than Arabic numbers, you must type {\tt\char`\\romanchapternum} before the {\tt\char`\\title} line. The chapter title and the current, main-level heading title appear in the appropriate running heads automatically. If the full title or heading would require more than one line to fit in the running head, an abbreviated form, including the correct chapter or section number, should be substituted using {\tt\char`\\leftheadtext} or {\tt\char`\\rightheadtext} respectively. The \hbox{\tt\char`\\leftheadtext} should be typed after the {\tt\char`\\endtopmatter} command and any \hbox{\tt\char`\\rightheadtext} should be typed after the appropriate {\tt\char`\\head} command. \subhead 1.2. 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 1.3. 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 2.1} 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 \item"(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