期刊
SPRINGERPLUS
卷 5, 期 -, 页码 -出版社
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1186/s40064-016-3255-5
关键词
Fuzzy set; Convex space; Stratified L-convex space; Embedding functor; Subcategory
资金
- National Natural Science Foundation of China [11501278]
- Shandong Provincial Natural Science Foundation, China [ZR2013AQ011, ZR2014AQ011]
- Ke Yan Foundation of Liaocheng University [318011505]
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.
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