Boolean spaces

http://mathcs.chapman.edu/structuresold/files/Boolean_spaces.pdf

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\newtheorem*{morphisms}{Morphisms}
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\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}

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

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