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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]]
+)]
+
+