Booleanization of a locale
= Booleanization of a locale
{title2=$X_b,\quad\mathcal O(X_b)=\mathcal O(X)_{\neg\neg}$}
= Boolean part of a locale
{synonym}
The double-negation <nucleus on a frame> gives a <dense sublocale> whose <frame> is a <complete Boolean algebra>. Its elements are <regular open elements>, with Boolean joins $\neg\neg\bigvee_i a_i$.