6533b82ffe1ef96bd1295aa2

RESEARCH PRODUCT

Sobriety and spatiality in categories of lattice-valued algebras

Sergey A. Solovyov

subject

Discrete mathematicsInterior algebraSobrietyArtificial IntelligenceLogicMathematics::General TopologyGeneral topologyTopological spaceEquivalence (formal languages)Mathematics

description

The paper provides an analogue of the famous equivalence between the categories of sober topological spaces and spatial locales for the framework of (L,M)-fuzzy topology of Kubiak and Sostak (and partly to that of Guido). To be more general, we replace locales with localic lattice-valued algebras in the sense of Di Nola and Gerla and use the respective generalized topological setting. As a result, it appears that the shift from crisp algebras to lattice-valued algebras weakens (resp. strengthens) considerably the classical (including the point-set lattice-theoretic setting of Rodabaugh) notion of sobriety (resp. spatiality).

yearjournalcountryeditionlanguage
2012-10-01Fuzzy Sets and Systems
https://doi.org/10.1016/j.fss.2012.04.018