Geodesic
Semilattices with sectional mappings
Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 1, pp. 11-19

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We consider join-semilattices with 1 where for every element p a mapping on the interval [p,1] is defined; these mappings are called sectional mappings and such structures are called semilattices with sectional mappings. We assign to every semilattice with sectional mappings a binary operation which enables us to classify the cases where the sectional mappings are involutions and / or antitone mappings. The paper generalizes results of [3] and [4], and there are also some connections to [1].
Keywords: semilattice, sectional mapping, antitone mapping, switching mapping, involution 
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Chajda, Ivan; Eigenthaler, Günther. Semilattices with sectional mappings. Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 1, pp. 11-19. http://geodesic.mathdoc.fr/item/DMGAA_2007_27_1_a0/