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A continuous $3$-distributive frame that is not $ω$-distributive
We give a negative answer to the question, posed by Erné, whether every $3$-distributive lattice is $ω$-distributive. More precisely, we exhibit a continuous frame that is $κ$-distributive for every integer $κ\geq 2$, but is not a wide coframe. The frame is the open-set lattice of a compact, locally
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