Abstract
We show that, in any topological space, boolean combinations of open sets have a canonical representation as a finite union of locally closed sets. As an application, if $\mathfrak M$ is a first-order topological structure, then sets definable in $\mathfrak M$ that are boolean combinations of open sets are boolean combinations of open definable sets.
Citation
Randall Dougherty. Chris Miller. "Definable Boolean combinations of open sets are Boolean combinations of open definable sets." Illinois J. Math. 45 (4) 1347 - 1350, Winter 2001. https://doi.org/10.1215/ijm/1258138070
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