% FILE: example_1.tex
%
% SYNOPSIS:
% This is Example 1 of the usage of the New Font Selection Scheme
% (NFSS) together with the American Mathematical Society Fonts
% (AMSFonts). It is a LaTeX file and no alterations/additions are
% needed to compile it.  However, both NFSS (with the fontdef.max
% option) and AMSFonts must be installed. Also the following files
% (coming with AMSFonts and/or AMS-LaTeX) should be available
%       amssymb.sty
%       amsfonts.sty
%       amsbsy.sty
%       amstext.sty
%       cyracc.def
%
%%% This example shows how to define fonts for use in *math mode*.
%
% The fonts used are the ones provided by AMSFonts, namely
%   Euler fraktur
%     (AMSFonts files: eufm5,eufm6,eufm7,eufm8,eufm9,eufm10)
%   Euler fraktur bold
%     (AMSFonts files: eufb5,eufb6,eufb7,eufb8,eufb9,eufb10)
%   Euler roman
%     (AMSFonts files: eurm5,eurm6,eurm7,eurm8,eurm9,eurm10)
%   Euler roman bold
%     (AMSFonts files: eurb5,eurb6,eurb7,eurb8,eurbr,eurb10)
%   Euler script
%     (AMSFonts files: eusm5,eusm6,eusm7,eusm8,eusm9,eusm10)
%   Euler script bold
%     (AMSFonts files: eusb5,eusb6,eusb7,eusb8,eusb9,eusb10)
%   University of Washington Cyrillic
%     (AMSFonts files: wncyr5,wncyr6,wncyr7,wncyr8,wncyr9,wncyr10)
%   University of Washington Cyrillic bold
%     (AMSFonts files: wncyb5,wncyb6,wncyb7,wncyb8,wncyb9,wncyb10)
%   Blackboard Bold
%     (AMSFonts files: msbm5,msbm6,msbm7,msbm8,msbm9,msbm10)
% Compare also Table 5, p. 14 of ``AMS-LaTeX Version 1.1 User's
% Guide'', American Mathematical Society, August 1991.

\documentstyle[11pt,newlfont,amssymb,amsbsy]{article}
                % amssymb.sty loads amsfonts.sty
                % amsbsy.sty loads amstext.sty

                % Also [newlfont,amssymb,amsbsy]
                % and  [12pt,newlfont,amssymb,amsbsy]
                % will work smoothly with the definitions below

   \input{cyracc.def} % This file is needed for cyrillic fonts

   % The following commands should produce proper results.
   % To understand how to type Russian when using cyracc.def see
   % the AMSFonts user's guide (section `Cyrillic input', pp. 15--16).

   \newmathalphabet{\eufm}                      % Euler
   \addtoversion{normal}{\eufm}{euf}{m}{n}      %       fraktur
   \addtoversion{bold}{\eufm}{euf}{b}{n}        %       fraktur bold
                % Define command \eufm as Euler fraktur font
                % to be used in math mode. It is already defined
                % in amsfonts.sty as \frak.

   \newmathalphabet{\eurm}                      % Euler
   \addtoversion{normal}{\eurm}{eur}{m}{n}      %       roman
   \addtoversion{bold}{\eurm}{eur}{b}{n}        %       roman bold
                % Define command \eurm as Euler roman font
                % to be used in math mode.

   \newmathalphabet{\eusm}                      % Euler
   \addtoversion{normal}{\eusm}{eus}{m}{n}      %       script
   \addtoversion{bold}{\eusm}{eus}{b}{n}        %       script bold
                % Define command \eusm as Euler script font
                % to be used in math mode.

   \newmathalphabet{\cyr}                       % Univ. of Washington
   \addtoversion{normal}{\cyr}{UWCyr}{m}{n}     %       cyrillic
   \addtoversion{bold}{\cyr}{UWCyr}{b}{n}       %       cyrillic bold
                % Define command \cyr as University of Washington
                % Cyrillic to be used in math mode.

   % ====================================================================

   % To get bold in math use command \boldsymbol{} provided
   % by amsbsy.sty file. See examples in text.

\title{Examples of Application of NFSS to Define and Use AMSFonts
in Math Mode}
\author{\bf Rafa\l\ \.Zbikowski}
\date{June, 1992}
\begin{document}

\maketitle

\section{Introduction}

This brief document shows four examples of defining fonts for use
in math mode using the New Font Selection Scheme (NFSS).
The fonts employed are those provided with the American Mathematical
Society (AMS) package AMSFonts Version 2.1. These are
\begin{itemize}
  \item Euler fraktur,
  \item Euler roman,
  \item Euler script,
  \item University of Washington cyrillic,
\end{itemize}
and also Blackboard bold. It is shown here how to use all the fonts
both in normal and bold versions (except for Blackboard bold,
which doesn't have a bold version).

The following commands are defined
\begin{itemize}
   \item \verb+\eufm+ for Euler fraktur medium (as opposed to bold),
   \item \verb+\eurm+ for Euler roman medium,
   \item \verb+\eusm+ for Euler script medium,
   \item \verb+\cyr + for University of Washington cyrillic medium.
\end{itemize}
There is also a predefined one \verb+\Bbb+ (see {\bf Example 4}).
Their effective definitions are shown at the end of this document.  To
make use of the above-mentioned fonts the following style files
should be loaded {\tt amsbsy.sty, amstext.sty, cyracc.def}. This
document also makes use of {\tt amssymb.sty} and {\tt amsfonts.sty}
to take a full advantage of extended math symbols set provided by
AMSFonts 2.1.  The use of an extra symbol is marked by \checkmark ,
itself a (nonmathematical) symbol from AMSFonts 2.1.

\section{Examples}

This section shows four simple examples of usage of the commands in
math mode.

{\bf Example 1}\newline
[ Here Euler script is used for the capital O, through a \verb+\eusm+
command and the symbol of the empty set \verb+\varnothing+ is used
from the extra math symbols B font. ]

{\sc Definition} Let $ X $ be a non-empty set. Then the pair
$ (X,\eusm{O}) $ is called a {\em topological space\/} iff
\begin{enumerate}
   \item $ X $ is open,
   \item $ \varnothing $ \checkmark is open,
   \item $ \eusm{O} $ is an open family of subsets
          of $ X $, i.e.
         \begin{enumerate}
            \item $ \forall \eusm{O}_i \in \eusm{O} $ the intersection
                  of a finite number of members of $ \eusm{O} $, i.e.
                  $ \bigcap_{i=1}^n \eusm{O}_i $, is open,
            \item $ \forall \eusm{O}_i \in \eusm{O} $ the union (finite or
                  infinite) of members of $ \eusm{O} $, i.e.
                  $ \bigcup_{i=1}^{\infty} \eusm{O}_i $, is open.
         \end{enumerate}
\end{enumerate}
The family $ \eusm{O} $ is called a {\em topology on\/} $ X $. $ \Box $

{\bf Example 2}\newline
[ Here Euler fraktur \verb+\eufm+ is used for the capital A, Euler
roman \verb+\eurm+ for the capital J; the symbol of (non-strict)
precedence \verb+\preccurlyeq+ comes from the extra math symbols A
font. ]

{\sc Proposition} Let $ (A,\preccurlyeq) $ \checkmark be
a well-ordered set. Then the family $ \eufm{A} $ of all
initial segments of $ A $, i.e. $ \eufm{A} = \{ \eurm{J}\subset A | \;
\forall x,y \in A \; ((y \in \eurm{J}) \wedge (x \preccurlyeq y))
\Rightarrow (x \in \eurm{J}) \}$, together with the relation
$ \subseteq $ is also a well-ordered set. $ \Box $

{\bf Example 3}\newline
[ Here University of Washington cyrillic \verb+\cyr+ is used (for the
Russian `Sh' letter) and the solid Halmos' symbol \verb+\blacksquare+
comes from the extra math symbols A font. ]

{\sc Notation} We shall denote by $ \cyr{Sh} $ the Shafarevich group
and we shall use $ \cyr{sh}_1,\ldots,\cyr{sh}_n $ for its subgroups.
$ \blacksquare $ \checkmark

{\bf Example 4}\newline
[ Here the use of bold mode of Euler roman \verb+\eurm+ is shown
via \verb+\boldsymbol+ command. Also Blackboard bold font \verb+\Bbb+,
defined in {\tt amsfonts.sty}, is used to denote the set of
real numbers. Finally, two extra symbols are displayed
\verb+\blacktriangleright+ and \verb+\bigstar+, both from
the extra math symbols A font. ]

$ \blacktriangleright $ \checkmark {\sc Exercise} Let
$ \boldsymbol{\eurm{f(x,y) = 0}} $ be given with
$ \boldsymbol{\eurm{x}} \in \Bbb{R}^n $ and $ \boldsymbol{\eurm{y}} \in
\Bbb{R}^m $.  State a sufficient condition for the existence of $
\boldsymbol{\eurm{g}}\colon \Bbb{R}^n \rightarrow \Bbb{R}^m $, such
that $ \boldsymbol{\eurm{y = g(x)}}$ (The Implicit Function Theorem).
$ \bigstar $ \checkmark

\section{Commands' Definitions}

The command \verb+\Bbb+ is defined in the file {\tt amsfonts.sty.sty}.
Also a counterpart of \verb+\eufm+ is predefined in {\tt amsfonts.sty}
as \verb+\frak+.

The verbatim definitions used in this document look as follows
\begin{verbatim}
\newmathalphabet{\eufm}                  % Euler
\addtoversion{normal}{\eufm}{euf}{m}{n}  %       fraktur
\addtoversion{bold}{\eufm}{euf}{b}{n}    %       fraktur bold
             % Define command \eufm as Euler fraktur font
             % to be used in math mode. It is already defined
             % in amsfonts.sty as \frak.

\newmathalphabet{\eurm}                  % Euler
\addtoversion{normal}{\eurm}{eur}{m}{n}  %       roman
\addtoversion{bold}{\eurm}{eur}{b}{n}    %       roman bold
             % Define command \eurm as Euler roman font
             % to be used in math mode.

\newmathalphabet{\eusm}                  % Euler
\addtoversion{normal}{\eusm}{eus}{m}{n}  %       script
\addtoversion{bold}{\eusm}{eus}{b}{n}    %       script bold
             % Define command \eusm as Euler script font
             % to be used in math mode.

\newmathalphabet{\cyr}                   % Univ. of Washington
\addtoversion{normal}{\cyr}{UWCyr}{m}{n} %       cyrillic
\addtoversion{bold}{\cyr}{UWCyr}{b}{n}   %       cyrillic bold
             % Define command \cyr as University of Washington
             % Cyrillic to be used in math mode.
\end{verbatim}

\end{document}

>>>>>>>>>>>>>>>>>>>>>>>>> END Example 1
