Affiliations: [a] College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China | [b] Department of Mathematics, Liaocheng University, Liaocheng, P.R. China
Correspondence:
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Corresponding author. Qingguo Li, College of Mathematics and Econometrics, Hunan University, Changsha, 410082, P.R. China. liqingguoli@yahoo.com.cn
Abstract: By making use of fuzzy inclusion order, the notions of bases (subbases) for three enriched L-topologies including stratified L-topologies, strong L-topologies and Alexandrov L-topologies, are presented. Some characterizations for these notions are given. The results exhibit many different features from the base (subbase) in L-topologies. Some non-trivial examples including a base for the topologically generated (stratified, strong) L-topologies and a base for the Alexandrov L-topologies derived from L-fuzzy rough sets, are constructed. At last, an application in open and continuous functions is offered.
