Affiliations: [a] College of Mathematics Science, Inner Mongolia Normal University, Hohhot, P.R. China
| [b] College of Science, Tianjin University of Technology and Education, Tianjin, P.R. China
Correspondence:
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Corresponding author. Rui-Ying Wang, College of Science, Tianjin University of Technology and Education, Tianjin, P.R. China. E-mail: [email protected].
Abstract: Connectivity is one of the most essential notions in general topology. Convex structures are topological-like structures. Many properties in topological spaces have been generalized to convex structures, such as separation. However, connectivity has not been studied in convex structures yet. In this paper, firstly, based on the consideration to hull operators, separatedness is defined in classical convex structures, and then we provide the concept of connectivity. Secondly, some equivalent characterizations of connectivity are discussed, and we investigate the related properties of connectivity. In additional, through (L, M)-fuzzy convex hull operators, we propose the separatedness degrees of (L, M)-fuzzy convex structures. Furthermore, the notion of connectedness degrees of (L, M)-fuzzy convex structures is introduced. Finally, many properties of connectivity in general convex structures can be generalized to (L, M)-fuzzy convex structures.
