Geodesic
Some lattices of closure systems on a finite set
Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 2.

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In this paper we study two lattices of significant particular closure systems on a finite set, namely the union stable closure systems and the convex geometries. Using the notion of (admissible) quasi-closed set and of (deletable) closed set, we determine the covering relation \prec of these lattices and the changes induced, for instance, on the irreducible elements when one goes from C to C' where C and C' are two such closure systems satisfying C \prec C'. We also do a systematic study of these lattices of closure systems, characterizing for instance their join-irreducible and their meet-irreducible elements. 
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     title = {Some lattices of closure systems on a finite set},
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Caspard, Nathalie; Monjardet, Bernard. Some lattices of closure systems on a finite set. Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 2. doi : 10.46298/dmtcs.309. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.309/

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