% This file requires static.pdf and rotation.avi
% It should be processed twice by pdflatex.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Topology Proceedings Sample Latex Article %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[10]{amsart}
\usepackage[T1]{fontenc} %%%%%%%Please do not change
\usepackage{graphics} %%%%%%%
\usepackage{movie15}
\usepackage[draft]{hyperref}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Please do not change this paragraph. %%%%%%%
\setcounter{page}{1} %%%%%%%
\setlength{\textwidth}{4.4in} %%%%%%%
\setlength{\textheight}{7.0in} %%%%%%%
\setlength{\evensidemargin}{1in} %%%%%%%
\setlength{\oddsidemargin}{1in} %%%%%%%
\setlength{\topmargin}{.8in} %%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Please do not change the page size %%%%%%%
% and do not redefine the baselineskip.%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{remark}[theorem]{Remark}
\numberwithin{equation}{section}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This a placeholder for the TOPLOGY PROCEEDINGS logo %%%%%%
\noindent %%%%%%
\begin{picture}(150,36) %%%%%%
\put(5,20){\tiny{Submitted to}} %%%%%%
\put(5,7){\textbf{Topology Proceedings}} %%%%%%
\put(0,0){\framebox(140,34){}} %%%%%%
\put(2,2){\framebox(136,30){}} %%%%%%
\end{picture} %%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace{0.5in}
\renewcommand{\bf}{\bfseries}
\renewcommand{\sc}{\scshape}
%insert defs/styles
\vspace{0.5in}
\title[Topology Proceedings Example Article]%
{Topology Proceedings \\Example for the Authors}
% Information for first author:
\author{Author One}
\address{Department of Mathematics \& Statistics; Auburn University;
Auburn, Alabama 36849}
% Current address (if needed):
%\curraddr{}
\email{topolog@auburn.edu}
%\thanks{The first author was supported in part by NSF Grant \#000000.}
% Information for second author (if needed):
%\author{Author Two}
%\address{}
%\email{}
%\thanks{Support information for the second author.}
% General info
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subjclass[2010]{Primary 54X10, 58Y30, 18D35; Secondary 55Z10}
% %
% Please use the current 2010 Mathematics Subject Classification:
% http://www.ams.org/mathscinet/msc/
% http://www.zentralblatt-math.org/msc/en/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\keywords{Some objects, some conditions}
\thanks {ALL references are real and correct; ALL citations are imaginary.}
\begin{abstract} This paper
contains a sample article in the Topology Proceedings format.
The article includes a simple example of a figure with an animation and a static graphic that shows instead of the animation when the file is printed.
\end{abstract}
\maketitle
\section{\bf Introduction}
This is a sample article in the TOPOLOGY PROCEEDINGS format.
Prepare your paper in a similar manner before submitting it
to TOPOLOGY PROCEEDINGS.
Please do not change the page size and do not redefine the other pagestyle
parameters like for example\newline
\noindent$\backslash$pagenumbering,
$\backslash$pagestyle,
$\backslash$baselineskip,
etc.
\section{\bf Including Animations}
This version of the article includes a simple example of a figure with an animation and a static graphic that shows instead of the animation when the file is printed (see Fig. \ref{rotationanim}).
To produce the PDF output file download the source files toproc-anim.tex, static.pdf and rotation.avi. Then process toproc-anim.tex twice by pdflatex.
Click on the figure to activate the animation. On some systems you may be asked to enable animations. In such a case, select the appropriate option and click on the figure again.
\begin{center}
\textsc{Guidelines for including animations:}
\end{center}
\noindent$\bullet$ We should be able to process your source files to get the final PDF. Please contact Topology Proceedings before submitting your paper if you wish to include animations using different packages than those in this example. Also, please contact us if your final PDF file is substantially bigger than 10 MB.
\noindent$\bullet$ Put your animations (and graphics) in the figure environment and let them float (be positioned automatically within the paper, \LaTeX{} default).
\noindent$\bullet$ Your animations and figures cannot be wider than the standard text width in the paper.
\noindent$\bullet$ Your paper must look good when printed on a 600 dpi black and white printer. The print version of TOPOLOGY PROCEEDINGS is in black and white only. To avoid white boxes in the printed version, each animation must be accompanied by a static graphic (or a graphic with text) that shows before the animation is run and also anytime the file is printed (see Fig. \ref{rotationanim}).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%FIGURE 1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% An example of including a figure with an animation and
%% a static pdf graphic to show in print instead of the animation
%% The file figure.pdf was exported from a graphic program.
%% Notice that the following 3 lines were added in the preamble.
%% \usepackage{graphics}
%% \usepackage{movie15}
%% \usepackage[draft]{hyperref}
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\begin{center}
\includemovie[text={
\scalebox{1.0}{\includegraphics{static.pdf}}}
]{288pt}{144pt}{rotation.avi}
\end{center}
\caption{An example animation. (Click in the figure to activate.)}\label{rotationanim}
\end{figure}
\section{\bf Main Results}
Let $\mathcal{S}$ denote the set of objects satisfying some condition.
\begin{definition}Let $n$ be a positive integer. An object has
the property $P(n)$ if
some additional condition involving the integer $n$ is satisfied.
We will denote
by $S_n$ the set of all $s$ in $\mathcal{S}$ with
the property $P(n)$.
\end{definition}
The following proposition is a simple consequence of the definition.
\begin{proposition}\label{Prop1}
The sets $S_1,S_2,\dots$ are mutually
exclusive.
\end{proposition}
\begin{lemma}
If $\mathcal{S}$ is infinite, then $\mathcal{S}=\bigcup_{n=1}^{\infty}S_n$.
\end{lemma}
\begin{proof}
Since $\mathcal{S}$ is the set of objects satisfying some condition,
it follows from \cite{A}
that
\begin{equation}\label{myeq}
\operatorname{obj}(\mathcal{S})<1.
\end{equation}
By \cite[Theorem 3.17]{E}, we have
\[
\operatorname{obj}(S_n)>2^{-n}
\]
for each positive integer $n$. This result, combined with (\ref{myeq}) and
Proposition \ref{Prop1}, completes the proof of the lemma.
\end{proof}
\begin{theorem}[Main Theorem]
Let $f:\mathcal{S}\to\mathcal{S}$ be a function such that
$f(S_n)\subset S_{n+1}$ for each positive integer $n$. Then the following
conditions are equivalent.
\begin{enumerate}
\item $\mathcal{S}=\emptyset$.
\item $S_n=\emptyset$ for each positive integer $n$.
\item $f(\mathcal{S})=\mathcal{S}$.
\end{enumerate}
\end{theorem}
\begin{remark} Observe that the condition in the definition
of $\mathcal{S}$ may be replaced by some other condition.
\end{remark}
\bibliographystyle{plain}
\begin{thebibliography}{10}
\smallskip
\bibitem{A} A. V. Arhangel'ski\u{i} and Scotty L. Thompson, {\it The cleavability approach to comparing topological spaces}, Questions Answers Gen. Topology {\bf 28} (2010), no. 2, 133--145.
\smallskip
\bibitem{B} Karol Borsuk, {\it On a new shape invariant}, Topology Proc. {\bf 1} (1976), 1--9.
\smallskip
\bibitem{E} Ryszard Engelking, {\it General Topology}. Translated from the Polish by the author. Monografie Matematyczne, Tom 60. [Mathematical Monographs, Vol. 60]. Warsaw: PWN---Polish Scientific Publishers, 1977.
\smallskip
\bibitem{K} Bronis\l av Knaster, {\it On applications of mathematical logic to mathematics} (Czech), \v{C}asopis P\v{e}st. Mat. {\bf 76} (1951), 3--22.
\smallskip
\bibitem{M} Kiiti Morita and Jun-iti Nagata, eds. {\it Topics in General Topology}. North-Holland Mathematical Library, 41. Amsterdam: North-Holland Publishing Co., 1989.
\smallskip
\bibitem{R} Mary Ellen Rudin, {\it A biconnected set in the plane}, Topology Appl. {\bf 66} (1995), no. 1, 41--48.
\smallskip
\bibitem{T} William P. Thurston, {\it On the geometry and dynamics of iterated rational maps}, in Complex Dynamics: Families and Friends. Ed. Dierk Schleicher. Wellesley, MA: A K Peters, 2009. 3--137.
\end{thebibliography}
\end{document}