Compatibilities between continuous semilattices

Keywords: conjugate capacity, continuous semilattice, monotonic predicate, compatibility
Published online: 2021-01-04


We define compatibilities between continuous semilattices as Scott continuous functions from their pairwise cartesian products to $\{0,1\}$ that are zero preserving in each variable. It is shown that many specific kinds of mathematical objects can be regarded as compatibilities, among them monotonic predicates, Galois connections, completely distributive lattices, isotone mappings with images being chains, semilattice morphisms etc. Compatibility between compatibilities is also introduced, it is shown that conjugation of non-additive real-valued or lattice valued measures is its particular case.

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How to Cite
Mykytsey O., Koporkh K. Compatibilities Between Continuous Semilattices. Carpathian Math. Publ. 2021, 13 (1), 5-14.