Mathematical Structures: Boolean spaces

# Boolean spaces

HomePage | RecentChanges | Login

http://mathcs.chapman.edu/structuresold/files/Boolean_spaces.pdf
%%run pdflatex

%

\documentclass[12pt]{amsart}
\usepackage[pdfpagemode=Fullscreen,pdfstartview=FitBH]{hyperref}
\parindent=0pt
\parskip=5pt
\addtolength{\oddsidemargin}{-.5in}
\addtolength{\evensidemargin}{-.5in}
\addtolength{\textwidth}{1in}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem*{morphisms}{Morphisms}
\newtheorem*{basic_results}{Basic Results}
\newtheorem*{examples}{Examples}
\newtheorem{example}{}
\newtheorem*{properties}{Properties}
\newtheorem*{finite_members}{Finite Members}
\newtheorem*{subclasses}{Subclasses}
\newtheorem*{superclasses}{Superclasses}
\newcommand{\abbreviation}[1]{\textbf{Abbreviation: #1}}
\hyperbaseurl{http://math.chapman.edu/structures/files/}
\pagestyle{myheadings}\thispagestyle{myheadings}
\markboth{\today}{math.chapman.edu/structures}

\begin{document}
\textbf{\Large Boolean spaces}
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Boolean_spaces}{edit}

\abbreviation{BSp}

\begin{definition}
A \emph{Boolean space} is a \href{Compact_Hausdorff_topological_spaces.pdf}{compact Hausdorff topological space} $\mathbf{X}=\langle X,\Omega\rangle$ that is \emph{totally disconnected}:

any two distinct points are separated by a clopen set ($\forall x\ne y\in X\exists U\in\Omega (x\in X\text{ and }y\in X\setminus U\in\Omega)$).
\end{definition}

\begin{morphisms}
Let $\mathbf{X}$ and $\mathbf{Y}$ be Boolean spaces. A morphism from $\mathbf{X}$ to $\mathbf{X}$ is a function $h:X\rightarrow Y$ that is continious:
$\forall V\in\Omega_{\mathbf{Y}}\ h^{-1}[V]\in\Omega_{\mathbf{X}}$.
\end{morphisms}

\begin{basic_results}
\end{basic_results}

\begin{examples}
\begin{example}
\end{example}
\end{examples}

\begin{table}[h]
\begin{properties} (\href{http://math.chapman.edu/cgi-bin/structures?Properties}{description})

\begin{tabular}{|ll|}\hline
Classtype                       & second-order \\\hline
Amalgamation property           & \\\hline
Strong amalgamation property    & \\\hline
Epimorphisms are surjective     & \\\hline
\end{tabular}
\end{properties}
\end{table}

\begin{finite_members} All finite discrete topological spaces.
\end{finite_members}

\begin{subclasses}\

\href{....pdf}{...} subvariety

\href{....pdf}{...} expansion

\end{subclasses}

\begin{superclasses}\

\href{....pdf}{...} supervariety

\href{....pdf}{...} subreduct

\end{superclasses}

\begin{thebibliography}{10}

\bibitem{Ln19xx}
F. Lastname, \emph{Title}, Journal, \textbf{1}, 23--45 \href{http://www.ams.org/mathscinet-getitem?mr=12a:08034}{MRreview}

\end{thebibliography}

\end{document}
%

HomePage | RecentChanges | Login
This page is read-only | View other revisions
Last edited July 8, 2004 1:19 pm by Jipsen (diff)
Search: