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Abstract :
[en] In a Boolean algebra, the "contact" and "nontangential part-of" relations are linked and interdefinable thanks to the complement. These relations yield on the Stone dual of the algebra two closed relations that appear to be the same. In a distributive lattice, the contact and nontangential part-of relations also yield dual closed relations on the Priestley dual. However, as the link between them is lost, these relations are not equal anymore. We explore the conditions linking the contact and nontangential part-of relations one should add in order to recover these relations knowing the intersection of their dual.