\noindent This space has the following properties:
\begin{enumerate}
\item Grade 2 Cantor\label{Cantor}
\item Half-smooth Hausdorff\label{Hausdorff}
\item Metrizably smooth\label{smooth}
\end{enumerate}
Therefore, we can apply the Main Theorem \ldots
% 3.1.2 Bulleted lists: itemize
\noindent In this lecture, we set out to accomplish a variety
of goals:
\begin{itemize}
\item To introduce the concept of smooth functions
\item To show their usefulness in the differentiation
of Howard-type functions
\item To point out the efficacy of using smooth functions
in Advanced Calculus courses
\end{itemize}
% 3.1.3 Captioned lists: description
In this introduction, we outline the history of this concept.
The main contributors were:
\begin{description}
\item[J. Perelman,] the first to introduce smooth functions.
\item[T. Kov\'acs,] who showed their usefulness in the
differentiation of Howard-type functions.
\item[A.P. Fein,] the main advocate of using smooth
functions in Advanced Calculus courses.
\end{description}
In addition to these mathematicians \ldots
% 3.1.4 Rule and combinations
\begin{enumerate}
\item First item of Level 1.
\begin{enumerate}
\item First item of Level 2.
\begin{enumerate}
\item First item of Level 3.
\begin{enumerate}
\item First item of Level 4.\label{level4}
\item Second item of Level 4.
\end{enumerate}
\item Second item of Level 3.
\end{enumerate}
\item Second item of Level 2.
\end{enumerate}
\item Second item of Level 1.
\end{enumerate}
Referencing the first item of Level 4: \ref{level4}
\begin{enumerate}
\item First item of Level 1.
\begin{itemize}
\item First item of Level 2.
\begin{enumerate}
\item First item of Level 3.
\begin{itemize}
\item First item of Level 4.\label{enums}
\item Second item of Level 4.
\end{itemize}
\item Second item of Level 3.
\end{enumerate}
\item Second item of Level 2.
\end{itemize}
\item Second item of Level 1.
\end{enumerate}
Referencing the first item of Level 4: \ref{enums}
\begin{tabbing}
This is short.\=\\
This is much longer, \> and jumps back.
\end{tabbing}
% 3.3 Miscellaneous displayed text environments
\begin{quote}
It's not that I'm afraid to die. I just don't want to be
there when it happens.
\emph{Woody Allen}
Literature is news that STAYS news. \emph{Ezra Pound}
\end{quote}
\begin{quotation}
KATH: Can he be present at the birth of his child?
ED: It's all any reasonable child can expect if the dad
is present at the conception.
\begin{flushright}
\emph{Joe Orton}
\end{flushright}
\end{quotation}
\begin{verse}
I think that I shall never see\\
A poem as lovely as a tree.
Poems are made by fools like me,\\
But only God can make a tree.
\begin{verbatim}
Formula (2) in section 3 should be typed as follows:
\begin{equation}
D^{\langle 2 \rangle} = \{\, \langle x_0, x_1 \rangle
\mid x_0, x_1 \in D,\ x_0 = 0 \Rightarrow x_1 = 0 \,\}.
\end{equation}
Please make the corrections.
\end{verbatim}
Some European e-mail addresses contain \texttt{\%};
recall that you have to type \verb+\%+ to get \texttt{\%}.
% 3.4 Proclamations (theorem-like structures)
\begin{definition}\label{D:prime}
\begin{enumerate}
\item $u$ is \emph{meet-irreducible} if
$u = x \wedge y$ implies that
$u = x$ or $u = x$.\label{mi1}
\item $u$ is \emph{meet-irreducible} if
$u = x \wedge y$ implies that
$u = x$ or $u = x$.\label{mi2}
\item $u$ is \emph{completely join-irreducible} if
$u = \bigvee X$ implies that $u \in X$.
\label{mi3}
\end{enumerate}
\end{definition}
\begin{xca}
Prove that if $\inf H$ exists for all nonempty subsets $H$ of a
poset $P$, then $\sup \varnothing$ also exists in~$P$.
\end{xca}
\begin{xcb}{Exercises}
\begin{enumerate}
\item A finite lattice $L$ is modular if{f} it does not
contain a pentagon.\label{E:pentagon}
\item Can the numbers of covering pairs in
Exercise~\ref{E:pentagon} be increased?\label{E:increased}
\end{enumerate}
\end{xcb}
% 3.5 Proof environment
\begin{proof}
This is the proof, delimited by the q.e.d. symbol.
\end{proof}
\begin{proof}[Necessity]
This is the proof of necessity.
\end{proof}
\begin{proof}
Now the proof follows from the equation
\[
a^2 = b^2 + c^2.\qedhere
\]
\end{proof}
% 3.7 Tabular environment
\begin{tabular}{ | l | r | r | r | }
\hline
Name & 1 & 2 & 3 \\ \hline
Peter & 2.45 & 34.12 & 1.00\\ \hline
John & 0.00 & 12.89 & 3.71\\ \hline
David & 2.00 & 1.85 & 0.71\\ \hline
\end{tabular}
\begin{table}
\begin{center}
\begin{tabular}{ || l | r | r | r || }
\hline
Name & 1 & 2 & 3 \\ \hline
Peter & 2.45 & 34.12 & 1.00\\ \hline
John & 0.00 & 12.89 & 3.71\\ \hline
David & 2.00 & 1.85 & 0.71\\ \hline
\end{tabular}
\caption{Tabular table}\label{Ta:first}
\end{center}
\end{table}
\begin{flushright}
The \begin{bfseries}simplest\end{bfseries}
text environments set the
printing style and size.\\
The commands and the environments have similar names.
\end{flushright}
% 9.6 Custom lists
% 9.6.2 The list environment
\noindent Here are the most important \LaTeX\ rules about
spaces in text, sentences, and paragraphs:
\begin{list}{$\diamondsuit$}{\setlength{\leftmargin}{.5in}
\setlength{\rightmargin}{.5in}}
\item \textbf{Rule 1:} Two or more spaces in text are
the same as one.
\item \textbf{Rule 2:} A blank line (that is, two end-of-line
characters separated only by blanks and tabs) indicates
the end of a paragraph.
\end{list}
Rules 1 and~2 make typing and copying very convenient.
\noindent Here are the most important \LaTeX\ rules about
spaces in text, sentences, and paragraphs:
\begin{list}{}{\setlength{\leftmargin}{.5in}
\setlength{\rightmargin}{.5in}}
\item[\textbf{Rule 1:}] Two or more spaces in text are
the same as one.
\item[\textbf{Rule 2:}] A blank line (that is, two
end-of-line characters separated only by blanks and tabs)
indicates the end of a paragraph.
\end{list}
Rules 1 and~2 make typing and copying very convenient.
% Using counters
Here are the most important \LaTeX\ rules about spaces in text,
sentences, and paragraphs:
\newcounter{spacerule}
\begin{list}{\textbf{Rule \arabic{spacerule}:}}
{\setlength{\leftmargin}{.5in}
\setlength{\rightmargin}{.5in}
\usecounter{spacerule}}
\item Two or more spaces in text are
the same as one.
\item A blank line (that is, two end-of-line
characters separated only by blanks and tabs) indicates the end
of a paragraph.
\end{list}
Rules~1 and 2 make typing and copying very convenient.
% 9.6.3 Two complete examples
% Example 1
Here are the most important \LaTeX\ rules about spaces in text,
sentences, and paragraphs:
\newcounter{spacerule}
\begin{list}{\upshape \bfseries Rule \arabic{spacerule}:}
{\setlength{\leftmargin}{1.5in}
\setlength{\rightmargin}{.6in}
\setlength{\labelwidth}{1.0in}
\setlength{\labelsep}{.2in}
\setlength{\parsep}{0.5ex plus 0.2ex minus 0.1ex}
\setlength{\itemsep}{0ex plus 0.2ex minus 0ex}
\usecounter{spacerule}
\itshape}
\item Two or more spaces in text are the same as one.
\item A blank line (that is, two end-of-line characters
separated only by blanks and tabs) indicates the end
of a paragraph.
\end{list}
Rules~1 and 2 make typing and copying very convenient.
\newenvironment{myrules}
{\begin{list}
{\upshape \bfseries Rule \arabic{spacerule}:}
{\setlength{\leftmargin}{1.5in}
\setlength{\rightmargin}{.6in}
\setlength{\labelwidth}{1.0in}
\setlength{\labelsep}{.2in}
\setlength{\parsep}{0.5ex plus 0.2ex minus 0.1ex}
\setlength{\itemsep}{0ex plus 0.2ex minus 0ex}
\usecounter{spacerule}
\itshape} }
{\end{list}}
% Example 2
\begin{list}{}
{\setlength{\leftmargin}{30pt}
\setlength{\rightmargin}{0pt}
\setlength{\itemindent}{14pt}
\setlength{\labelwidth}{40pt}
\setlength{\labelsep}{5pt}
\setlength{\parsep}{0.5ex plus 0.2ex minus 0.1ex}
\setlength{\itemsep}{0ex plus 0.2ex minus 0ex}}
\item[\textbf{sentence}\hfill] is a group of words terminated
by a period, exclamation point, or question mark.
\item[\textbf{paragraph}\hfill] is a group of sentences
terminated by a blank line or by the \com{par} command.
\end{list}
% 9.7 Custom formats
\input tmplatex.ltx
\documentclass{article}
\usepackage{amssymb,latexsym,amsmath}
\dump
\end{verbatim}
On the other hand, the
\doc{sampartu.tex}\amssamplefileindex{sampartu.tex} article is a
little more complex:
\begin{verbatim}
\input tmplatex.ltx
\documentclass{amsart}
\usepackage{amssymb,latexsym}
\usepackage{lattice}
\newcommand{\Prodm}[2]{\gP(\,#1\mid#2\,)}
% product with a middle
\newcommand{\Prodsm}[2]{\gP^{*}(\,#1\mid#2\,)}
% product * with a middle
\newcommand{\vct}[2]{\vv<\dots,0,\dots,\overset{#1}{#2},%
\dots,0,\dots>}% special vector
\newcommand{\fp}{\F{p}}% Fraktur p
\newcommand{\Ds}{D^{\langle2\rangle}}
\dump
