## $$L$$-ordered neighborhood systems of stratified $$L$$-concave structures.(English)Zbl 1465.52004

Summary: Based on a complete residuated lattice $$L$$, the notion of stratified $$L$$-concave structures is introduced, which is the dual structure of convex structures in the $$L$$-setting. For characterizing it, $$L$$-ordered neighborhood systems and $$L$$-ordered interior operators in the framework of stratified $$L$$-concave spaces are introduced. Moreover, it is shown that $$L$$-ordered neighborhood spaces, $$L$$-ordered interior spaces and stratified $$L$$-concave spaces are isomorphic from the view of category.

### MSC:

 52A01 Axiomatic and generalized convexity 03E72 Theory of fuzzy sets, etc. 06A15 Galois correspondences, closure operators (in relation to ordered sets)
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