L-interval spaces and some of their properties

Article type: Research Article

Authors: Wu, Xiu-Yun^{a; b; *}

Affiliations: [a] School of Mathematics and Statistics, Anhui Normal University, Wuhui, China | [b] School of Science, HunanUniversity of Science and Engineering, Yongzhou, China

Correspondence: [*] Corresponding author. Xiu-Yun Wu. E-mail: wuxiuyun2000@126.cn.

Abstract: In this paper, notions of L-interval spaces and L-2-arity convex spaces are introduced. It is showed that there is a Galois’s connection between the category of L-convex spaces and the category of L-interval spaces. In particular, the category of L-2-arity convex spaces can be embedded in the category of L-interval spaces as a coreflective subcategory. Further, some properties of L-interval spaces are introduced including L-geometric (resp. L-Peano, L-Pasch and L-sand-glass) property. It is proved that an L-2-arity convex space is an L-JHC convex space iff its segment operator has L-Peano property. It is also proved that an L-JHC convex space with an L-idempotent segment operator has L-sand-glass property. Further, it is also proved that an L-idempotent interval space having L-Peano+L-Pasch property has L-geometric property and L-sand-glass property.

Keywords: L-convex space, L-2-arity convex space, L-interval space, L-geometric (Peano, Pasch, sand-glass) interval space

DOI: 10.3233/JIFS-182525

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 1, pp. 13-25, 2021