%----------------------------------------------------------------------------- % Beginning of CONM-P.let-e %----------------------------------------------------------------------------- Following this letter are three files (CONM-P.STY, CONM-P.TEX and CONM-P.CHECKLIST) to be used when preparing a paper 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-P style. Instructions for using this file are listed at the top. The .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 .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-P, please send the .TEX file 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-P.let-e %----------------------------------------------------------------------------- %----------------------------------------------------------------------------- % Beginning of conm-p.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-P 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-p.sty containing the data in the lines % from %%% conm-p.sty %%% through \endinput . Install the file % in the same directory as amsppt.sty . % % 2. In a data file, include the line, \documentstyle{conm-p} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 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@ \def\pretitle{\vskip7pc} % 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-P, we do want running heads. We must provide suitable % fonts definitions. CONM-P 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} % define a logo for the upper left-hand corner \def\jourlogo{\vbox to0pt{% \sixrm \baselineskip6pt \parindent0pt \frenchspacing Contemporary Mathematics\hfil\break Volume {\sixbf\cvol@}, \cvolyear@\par\vss}} % macros to be put into the \topmatter for the logo \def\cvol#1{\gdef\cvol@{\ignorespaces#1\unskip}} \def\cvolyear#1{\gdef\cvolyear@{\ignorespaces#1\unskip}} \def\cyear#1{\gdef\cyear@{\ignorespaces#1\unskip}\cyear@@#100000\end@} \def\cyear@@#1#2#3#4#5\end@{\gdef\cyearmodc@{#3#4}% \gdef\cyearmodcHold@{#3#4}} \cvol{00} \cyear{0000} \cvolyear{0000} \font\sixsy=cmsy6 \def\copyrightline@{\baselineskip1.75pc \rightline{% \vbox{\sixrm \textfont2=\sixsy \baselineskip 7pt \halign{\hfil##\cr \copyright\cyear@\ American Mathematical Society\cr 0000-0000/\cyearmodc@\ \$1.00 + \$.25 per page\cr }}}} \def\cyearmodc#1{\gdef\cyearmodc@{\ignorespaces#1\unskip}} % The copyright block takes the place of the AMS-TeX logo; otherwise the % AMSPPT.STY output routine does what we want. \let\logo@=\copyrightline@ % 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{\let\savedef@\title \def\title##1\endtitle{\let\title\savedef@\let\\=\cr \global\setbox\titlebox@\vtop{\titlefont\bf \raggedcenter@\frills@{##1}\endgraf}% \ifmonograph@ \edef\next{\the\leftheadtoks}\ifx\next\empty \leftheadtext{##1}\fi \fi \edef\next{\the\rightheadtoks}\ifx\next\empty \rightheadtext{##1}\fi }% \nofrillscheck\title} % authors are set in all caps \def\author#1\endauthor{\global\setbox\authorbox@ \vbox{\tenpoint\raggedcenter@ \expandafter\uppercase{\ignorespaces#1\endgraf}}\relaxnext@ \edef\next{\the\leftheadtoks}% \ifx\next\empty\expandafter\uppercase{\leftheadtext{#1}}\fi} \def\address#1\endaddress{\global\advance\addresscount@\@ne \expandafter\gdef\csname address\number\addresscount@\endcsname {\vskip12\p@ minus6\p@\indent\eightpoint{\smc\ignorespaces#1}\par}} % Current addresses as well as permanent ones must be accommodated. % Check on the skip before the address; it may be a fixed 6pt. % \smallskip has been assumed before the current address, as that % is what has been used for \email. \def\email{\let\savedef@\email \def\email##1\endemail{\let\email\savedef@ \toks@{\def\usualspace{{\it\enspace}}\endgraf\smallskip\indent\eightpoint}% \toks@@{##1\par}% \expandafter\xdef\csname email\number\addresscount@\endcsname {\the\toks@\frills@{{\noexpand\it E-mail address\noexpand\/}:% \noexpand\enspace}\the\toks@@}}% \nofrillscheck\email} \def\curraddr{\let\savedef@\curraddr \def\curraddr##1\endcurraddr{\let\curraddr\savedef@ \toks@\expandafter\expandafter\expandafter{% \csname address\number\addresscount@\endcsname}% \toks@@{##1}% \expandafter\xdef\csname address\number\addresscount@\endcsname {\the\toks@\endgraf\noexpand\nobreak \smallskip\indent\noexpand\eightpoint{\noexpand\rm \frills@{{\noexpand\it Current address\noexpand\/}:\space}% \def\noexpand\usualspace{\space}\the\toks@@\unskip}}}% \nofrillscheck\curraddr} % \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\indenti=3pc\noindent$$\vbox\bgroup \def\envir@end{\endabstract}\advance\hsize-2\indenti \def\usualspace{\enspace}\eightpoint \noindent \frills@{{\smc Abstract.\enspace}}}% \nofrillscheck\abstract} % \keywords, \subjclass and \thanks appear as first-page footnotes. % Reformat the top matter for CONM-P style. \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 \jourlogo \pretitle \vskip24\p@ plus12\p@ minus12\p@ \unvbox\titlebox@ \topskip10pt% reset to normal value \preauthor \ifvoid\authorbox@\else \vskip14\p@ plus6\p@ minus0\p@\unvbox\authorbox@\fi \predate \ifx\thedate@\empty\else \vskip6\p@ plus2\p@ minus0\p@ \line{\hfil\thedate@\hfil}\fi \preabstract \ifvoid\abstractbox@\else \vskip24\p@ plus12\p@ minus0\p@ \unvbox\abstractbox@ \fi \ifvoid\tocbox@\else\vskip1.5pc plus.5pc \unvbox\tocbox@\fi \prepaper \vskip24\p@ plus12\p@ minus0\p@} % 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}% \nofrillscheck\proclaim} \def\endproclaim{\revert@envir\endproclaim \par\rm \penaltyandskip@{55}\medskipamount} \def\demoheadfont@{\smc} \def\remarkheadfont@{\smc} \def\enddemo{\par\revert@envir\enddemo \endremark\vskip\z@ plus 1\p@\relax} \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\demo{\DN@{\ifx\next\nofrills \DN@####1####2{\remark####1{####2}\envir@stack\enddemo \ignorespaces}% \else \DN@####1{\remark{####1}\envir@stack\enddemo\ignorespaces}% \fi \next@}% \FN@\next@} % Roman type is needed within the statement of theorems for numerals, % fences, labels, etc. This definition should ultimately be in amsppt.sty. \def\rom#1{{\rm #1}} % \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} \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}}}} % Some patches are needed, to make \yr appear in translation information, % and to avoid the spurious unboxing of some empty boxes. % Add current address to \enddocument \outer\def\enddocument{\par% \par will do a runaway check for \endref \add@missing\endRefs \add@missing\endroster \add@missing\endproclaim \add@missing\enddefinition \add@missing\enddemo \add@missing\endremark \add@missing\endexample \ifmonograph@ % do nothing \else \nobreak \thetranslator@ \count@\z@ \loop\ifnum\count@<\addresscount@\advance\count@\@ne \csname address\number\count@\endcsname \csname email\number\count@\endcsname \repeat \fi \vfill\supereject\end} \catcode`\@=13 \def\amsversion{2.1} \endinput %----------------------------------------------------------------------------- % End of conm-p.sty %----------------------------------------------------------------------------- %----------------------------------------------------------------------------- % Beginning of conm-p.tex %----------------------------------------------------------------------------- % % AMS-TeX 2.1 sample file for CONM-P volumes. % \input amstex \documentstyle{conm-p} \NoBlackBoxes % \leftheadtext{AUTHOR ONE AND AUTHOR TWO} \rightheadtext{MAXIMAL IDEALS IN SUBALGEBRAS OF $C(X)$} \topmatter \title Sample Paper for CONM-P,\\ On Maximal Ideals in Subalgebras of $C(X)$\endtitle \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 % author two \endaddress % The following items give publication information for the CONM-P logo \cvol{00} \cvolyear{0000} \cyear{0000} % 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~2.1 preprint style with additional macros for the series {\bf CONM-P}. The file used to prepare this sample is {\bf CONM-P.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~2.1 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 can be best understood by examining the first part of the sample file {\bf CONM-P.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. The author names and the title that are to appear in the running heads should be input in all CAPS as {\tt\char`\\leftheadtext} and {\tt\char`\\rightheadtext} 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 that way. The author names should be input in caps and lowercase; they will automatically be set in all caps. For each author an address should be input. If the current address is different than the address where the research was carried out then both addresses are given with the current address second and coded as indicated in this sample file. Following these addresses, an address for electronic mail should be given, if one exists. Note that no abbreviations are used in addresses, and 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. Subject classifications ({\tt\char`\\subjclass}) and acknowledgments ({\tt\char`\\thanks}) are part of the top matter and will appear as 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. It is generally desirable not to attach footnote numbers or symbols to titles or author names used as headings. If a footnote applies to only one author then include this information in the footnote. Papers published in proceedings of conferences are often abstracts or preliminary versions. In such a case, include the following in the {\tt\char`\\thanks} to appear at the bottom of the first page: ``The final [detailed] version of this paper will be [has been] submitted for publication elsewhere.'' Papers that are to be considered for review by {\it Mathematical Reviews\/} should include the following statement: ``This paper is in final form and no version of it will be submitted for publication elsewhere.'' \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