A characterization of strong \(\mathcal{Q}\)-concave spaces. (English) Zbl 1465.52006

Shi, Yi; Huang, Han-Liang

J. Nonlinear Convex Anal. 21, No. 12, 2771-2781 (2020).

Summary: The concepts of strong \(\mathcal{Q}\)-concave structures and strong \(\mathcal{Q}\)-interior operators are proposed on quantale-valued setting. It is shown that the category of strong \(\mathcal{Q}\)-concave spaces is isomorphic to that of strong \(\mathcal{Q}\)-interior spaces.

MSC:

52A01	Axiomatic and generalized convexity
54A20	Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
06A15	Galois correspondences, closure operators (in relation to ordered sets)

Keywords:

fuzzy inclusion order; strong \(\mathcal{Q}\)-concavity; strong \(\mathcal{Q}\)-interior operator; fuzzy convexity; fuzzy concavity