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boolean_spaces [2010/07/29 15:23] (current)
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 +=====Boolean spaces=====
 +
 +Abbreviation: **BSp**
 +
 +====Definition====
 +A \emph{Boolean space} is a [[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 ($\forall x\ne y\in X\exists U\in\Omega (x\in X\text{ and }y\in X\setminus U\in\Omega)$).
 +
 +==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:
 +$\forall V\in\Omega_{\mathbf{Y}}\ h^{-1}[V]\in\Omega_{\mathbf{X}}$.
 +
 +====Examples====
 +Example 1:
 +
 +====Basic results====
 +
 +
 +====Properties====
 +^[[Classtype]]                        |second-order  |
 +^[[Amalgamation property]]            | |
 +^[[Strong amalgamation property]]     | |
 +^[[Epimorphisms are surjective]]      | |
 +
 +====Finite members====
 +
 +====Subclasses====
 +  [[...]] subvariety
 +
 +  [[...]] expansion
 +
 +
 +====Superclasses====
 +  [[...]] supervariety
 +
 +  [[...]] subreduct
 +
 +
 +====References====
 +
 +[(Ln19xx>
 +F. Lastname, \emph{Title}, Journal, \textbf{1}, 23--45 [[MRreview]]
 +)]
 +
 +