Questions tagged [frame-theory]

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In a frame, the closure of the intersection contains the closure of one sublocale intersect the other open sublocale

I want to prove that $\overline{W \cap S} \supseteq \overline{W} \cap S$ in a frame $L$, where $S$ is a open sublocale of the frame. My attempt; Let $y \in \overline{W} \cap S \Longrightarrow y \in {\uparrow} \bigwedge W \cap S \Longrightarrow y…