% Version of 12 September 1990

\catcode`@=11         %to allow use of @ as a letter; reset at the end

\magnification=\magstep1
\hsize=16.2truecm
\vsize=22.9truecm
%\hoffset=1.2truecm    %for book
%\voffset=0.4truecm    %for book
\baselineskip=15pt
\parindent=18pt
\abovedisplayskip=12pt plus 3pt minus 3pt
\belowdisplayskip=12pt plus 3pt minus 3pt
\abovedisplayshortskip=0pt plus 3pt
\belowdisplayshortskip=6pt plus 3pt

\def\lessraggedbottom{\topskip 10pt plus 10pt}
\lessraggedbottom

%\def\define{\def}   % for use with amstex
\def\predefine#1#2{\let#1#2}

%\def\Cal{\cal}      % for use with amstex

\font\fontzerorm=cmr10 at 10truept     %magstep0
\font\fontzerobf=cmbx10 at 10truept
\font\fonthalfrm=cmr10 at 11truept     %magstephalf
\font\fonthalfbf=cmbx10 at 11truept
\font\fontonerm=cmr10 at 12truept      %magstep1
\font\fontonebf=cmbx10 at 12truept
\font\fonttworm=cmr10 at 14.4truept    %magstep2
\font\fonttwobf=cmbx10 at 14.4truept
\font\fontthreerm=cmr10 at 17.3truept  %magstep3
\font\fontthreebf=cmbx10 at 17.3truept
\font\fontfourrm=cmr10 at 20.7truept   %magstep4
\font\fontfourbf=cmbx10 at 20.7truept
\font\fontfiverm=cmr10 at 24.9truept   %magstep5
\font\fontfivebf=cmbx10 at 24.9truept

%\font\sectionfont=cmbx10 scaled\magstep1  %for book
%\font\chapterfont=cmbx10 scaled\magstep3  %for book

\font\sevenzerorm=cmr7 at 7truept
\font\fivezerorm=cmr5 at 5truept
\font\fontzeromi=cmmi10 at 10truept
\font\sevenzeromi=cmmi7 at 7truept
\font\fivezeromi=cmmi5 at 5truept
\font\fontzerosy=cmsy10 at 10truept
\font\sevenzerosy=cmsy7 at 7truept
\font\fivezerosy=cmsy5 at 5truept
\font\fontzeroex=cmex10 at 10truept
\font\fontzeroti=cmti10 at 10truept

\def\abstractfont{\def\rm{\fam0\fontzerorm}%
 \textfont0=\fontzerorm \scriptfont0=\sevenzerorm
                        \scriptscriptfont0=\fivezerorm
 \textfont1=\fontzeromi \scriptfont1=\sevenzeromi
                        \scriptscriptfont1=\fivezeromi
 \textfont2=\fontzerosy \scriptfont2=\sevenzerosy
                        \scriptscriptfont2=\fivezerosy
 \textfont3=\fontzeroex \scriptfont3=\fontzeroex
                        \scriptscriptfont3=\fontzeroex
 \textfont\itfam=\fontzeroti \def\it{\fam\itfam\fontzeroti}%
 \textfont\bffam=\fontzerobf \def\bf{\fam\bffam\fontzerobf}%
 \normalbaselineskip=12truept
 \setbox\strutbox=\hbox{\vrule height8.5truept depth3.5truept width0truept}%
 \normalbaselines\rm}

\def\narrowertext{\advance\leftskip by 1.8truecm
               \advance\rightskip by 1.8truecm}
\newskip\myskipamount
   \myskipamount=10pt plus 1pt minus 1pt
\def\myskip{\vskip\myskipamount}
\def\mybreak{\par\ifdim\lastskip < \myskipamount\removelastskip
   \penalty-200\myskip\fi}

\outer\def\title{\vglue 24pt plus 3pt minus 3pt
                  \bgroup\tabskip\centering\halign to \hsize
                  \bgroup\tenbf\hfill\ignorespaces##
                  \unskip\hfill\cr}        % do not use \cr after last line
\def\endtitle{\cr\egroup\egroup\vskip\parskip}
\def\author#1\par{\vskip 18pt
                   \centerline{\bf#1}\vskip\parskip}
\def\myself{\vskip 18pt\centerline{\bf Christian Constanda}
             \vskip 3pt\centerline{Department of Mathematics}\vskip-1pt
                       \centerline{University of Strathclyde}\vskip-1pt
                       \centerline{Glasgow, Scotland, U.K.}\vskip 3pt}
\def\authorandaddress#1\par{\vskip 18pt\centerline{\bf #1}
             \vskip 3pt\centerline{Department of Mathematics}\vskip-1pt
                       \centerline{University of Strathclyde}\vskip-1pt
                       \centerline{Glasgow, Scotland, U.K.}\vskip 3pt}
\def\abstract{\vskip 18pt\bgroup\abstractfont\narrowertext\bgroup
                       \noindent\bf Abstract.\enspace
                       \rm\bgroup}
\def\endabstract{\egroup\par\egroup\egroup\vglue 3pt\vskip 15pt}
\outer\def\heading{\vskip 0pt plus .1\vsize\penalty-250
                    \vskip 0pt plus -.1\vsize
                    \bigbreak\bgroup\tabskip\centering
                    \halign to \hsize\bgroup\bf\hfill
                    \ignorespaces##\unskip\hfill\cr}
\def\endheading{\cr\egroup\egroup\nobreak\vskip 10pt}
\outer\def\section#1{\vskip 0pt plus .1\vsize\penalty-250
                     \vskip 0pt plus -.1\vsize
                     \bigbreak\leftline{\bf #1}
                     \vskip 9pt\noindent\ignorespaces}
\outer\def\subheading#1{\medbreak\noindent{\bf\ignorespaces
                        #1\unskip.\enspace}\ignorespaces}
\outer\def\proclaim#1{\mybreak\noindent\bf\ignorespaces
                      #1\unskip.\thinspace\it\ignorespaces\bgroup}
\outer\def\proclaimform#1{\noindent\bf\ignorespaces  %after formulae
                          #1\unskip.\thinspace\it\ignorespaces\bgroup}
\outer\def\endproclaim{\egroup\par\ifdim\lastskip<\myskipamount
                       \removelastskip\penalty 55\fi\myskip\rm}
\outer\def\endproclaimform{\egroup\par\rm}  %when theorem ends with formula
\outer\def\demo#1{\par\ifdim\lastskip<\medskipamount
                  \removelastskip\medskip\fi\noindent
                  {\bf\ignorespaces#1\unskip.\thinspace}\rm
                  \ignorespaces\begingroup}
\outer\def\demoform#1{\par\noindent  %when theorem ends with formula
                      {\bf\ignorespaces#1\unskip.\thinspace}\rm
                       \ignorespaces\begingroup}
\outer\def\enddemo{\endgroup\par\myskip}
\outer\def\enddemoform{\endgroup\par}  %when proof ends with formula
\def\paper{\vskip 36pt}

\def\more{\par\vskip 6pt\noindent}
\def\less{\par\vskip -5pt\noindent}

% The following are to be used for book-style page numbers:

%\footline={\ifodd\pageno\rightfootline\else\leftfootline\fi}
%\def\rightfootline{\tenrm\hfil\folio}
%\def\leftfootline{\tenrm\folio\hfil}

% Extras, to try in place of AMSTEX, but with most of its commands:

%\def\text#1{\hbox{\rm#1}}
%\def\align#1\endalign{\eqalignno{#1\cr}}
%\def\endalign{\null}
%\def\aligned#1\endaligned{\eqalign{#1\cr}}
%\def\endaligned{\null}
%\def\tag#1{\eqno({#1})}
%\def\flushpar{\noindent}
\def\frac#1#2{{#1\over#2}}
\def\dfrac{\displaystyle\frac}
\def\tfrac{\textstyle\frac}
%\def\operatorname#1{\hbox{\mathop#1}}
%\def\spreadlines{\openup}
\def\tsize{\textstyle}
\def\dsize{\displaystyle}

\def\titlepage{\ifnum\pageno=0\footline={\hfil}\else
               \footline={\hss\tenrm\folio\hss}\fi}

\newif\iftop@
\newif\ifbot@
\def\topsmash{\top@true\bot@false\smash@}
\def\botsmash{\top@false\bot@true\smash@}
\def\smash{\top@true\bot@true\smash@}
\def\smash@{\relax\ifmmode\def\next{\mathpalette\mathsm@sh}
   \else\let\next\makesm@sh\fi\next}
\def\finsm@sh{\iftop@\ht\z@\z@\fi\ifbot@\dp\z@\z@\fi\box\z@}
%\def\makesmash#1{\setbox0=\hbox{#1}\finsm@sh}
%\def\mathsm@sh#1#2{\setbox0=\hbox{$\m@th#1{#2}$}\finsm@sh}

%Next group is to avoid space between non-displayed formulae and
%following text when \mathsurround is not 0pt. But it doesn't seem to work.
%\def\carefulmathsurround{\everymath={\adjustmsurright}}
%\long\def\adjustmsurright#1${#1
%\global\futurelet\nextafter\adjustmsurrighta}
%\def\adjustmsurrighta{$\ifx-\nextafter\backupmsurr\fi
%\ifcat a\noexpand\nextafter\backupmsurr\fi}
%\def\backupmsurr{\nobreak\hskip-\mathsurround}
%\carefulmathsurround

%\def\makefootline{\baselineskip=27truept\line{\the\footline}}  %for book

%\def\dent#1{\setbox11=\hbox{#1\ }\par\hangindent=\wd11\hangafter=1
%            \noindent\box11}

\def\ps{{\it\$}}

\def\list{\bgroup\parindent=40pt\parskip=6pt}
%          \everypar={\hangindent=1.2truecm\hangafter=-100}}
\def\endlist{\par\egroup\medskip}
\def\varlist#1{\bgroup\parskip=6pt\parindent=#1truecm}
\def\endvarlist{\par\egroup\ifdim\lastskip<1truecm\removelastskip\medskip\fi}
\def\varitem{\par\hang\vartextindent}
\def\vartextindent#1{\indent\llap{\hbox to\hangindent{#1\hfil}}\ignorespaces}
\def\itemvar{\par\hang\textindentvar}
\def\textindentvar#1{\indent\llap{\hbox to\hangindent{\hfil#1
                      \thinspace}}\ignorespaces}

\def\pmb#1{\setbox0=\hbox{#1}%
           \kern-.025em\copy0\kern-\wd0
           \kern.05em\copy0\kern-\wd0
           \kern-0.025em\raise.0433em\box0}
\def\nix{{\phantom{0}}}

\def\boxit#1{\vbox{\hrule\hbox{\vrule\kern1pt
             \vbox{\kern1pt#1\kern1pt}\kern1pt\vrule}\hrule}}

\def\NoBlackBoxes{\global\overfullrule\z@}
%\NoBlackBoxes           % Use only for printing, after preview looks O.K.

\def\fnote#1#2{\let\@sf\empty % parameter #2 (the text) is read later
  \ifhmode\edef\@sf{\spacefactor=\the\spacefactor}\/\fi
  {$\,^{#1}$}\@sf\vfootnote{#1}{#2}}
\def\vfootnote#1#2{\insert\footins\bgroup
  \interlinepenalty\interfootnotelinepenalty
  \splittopskip=\ht\strutbox % top baseline for broken footnotes
  \splitmaxdepth=\dp\strutbox \floatingpenalty=20000
  \ifdim\lastskip<2truept \removelastskip\vskip 2truept\fi
  \leftskip=\parindent \rightskip=0pt \spaceskip=0pt \xspaceskip=0pt
  \baselineskip=11pt\parindent=0pt\abstractfont
  \textindent{$\,^{#1}$}#2\footstrut\vskip 3truept\egroup}

\catcode`@=12        %undoing of the initial move regarding @

\def\bull{\vrule height .9ex width .8ex depth - .1ex}%square bullet

%\footline={ifodd\pageno\rightfootline\else\leftfootline\fi}
%\def\rightfootline{\tenrm\hfil\folio}
%\def\leftfootline{\tenrm\folio\hfil}