title: On the embedding of convex spaces in stratified L-convex spaces.
abstract: Consider L being a continuous lattice, two functors from the category of convex spaces (denoted by CS) to the category of stratified L-convex spaces (denoted by SL-CS) are defined. The first functor enables us to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory. The second functor enables us to prove that the category CS can be embedded in the category SL-CS as a coreflective subcategory when L satisfying a multiplicative condition. By comparing the two functors and the well known Lowen functor (between topological spaces and stratified L-topological spaces), we exhibit the difference between (stratified L-)topological spaces and (stratified L-)convex spaces.
authors.affiliation: Department of Mathematics, Liaocheng University, Hunan Road, Liaocheng, 252059 People's Republic of China.
authors.forename: Qiu
authors.initials: Q
authors.lastname: Jin
authors.affiliation: Department of Mathematics, Liaocheng University, Hunan Road, Liaocheng, 252059 People's Republic of China.
authors.forename: Lingqiang
authors.initials: L
authors.lastname: Li
keywords: Convex space; Embedding functor; Fuzzy set; Stratified L-convex space; Subcategory