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Join congruence relations and closure relations

Authors:	Kenneth P Bogart Laura H Montague

Institution:	(1) Department of Mathematics, Dartmouth College, 03755 Hanover, NH, USA

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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