Abstract
In this paper we show that, given a complete lattice $$ \mathcal{L} $$ , the following three lattices are the same: (1) the lattice of closure relations on $$ \mathcal{L} $$ , (2) the lattice of meet-closed subsets of $$ \mathcal{L} $$ , and (3) the lattice of complete join congruence relations on $$ \mathcal{L} $$ .
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