Definable Boolean combinations of open sets are Boolean combinations of open definable sets

Dougherty, Randall; Miller, Chris

Illinois J. Math., Tome 45 (2001) no. 4, p. 1347-1350 / Harvested from Project Euclid

Résumé

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.

Publié le : 2001-10-15
Classification: 54A99, 03C64, 54H05

@article{1258138070,
     author = {Dougherty, Randall and Miller, Chris},
     title = {Definable Boolean combinations of open sets are Boolean combinations of open definable sets},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 1347-1350},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138070}
}

Dougherty, Randall; Miller, Chris. Definable Boolean combinations of open sets are Boolean combinations of open definable sets. Illinois J. Math., Tome 45 (2001) no. 4, pp.  1347-1350. http://gdmltest.u-ga.fr/item/1258138070/