Stratified L-prefilter convergence structures in stratified L-topological spaces
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In this paper, a new approach to fuzzy convergence theory in the framework of stratified L-topological spaces is provided. Firstly, the concept of stratified L-prefilter convergence structures is introduced and it is shown that the resulting category is a Cartesian closed topological category. Secondly, the relations between the category of stratified L-prefilter convergence spaces and the category of stratified L-topological spaces are studied and it is proved that the latter can be embedded in the former as a reflective subcategory. Finally, the relations between the category of stratified L-prefilter convergence spaces and the category of stratified L-Min convergence spaces (fuzzy convergence spaces in the sense of Min) are investigated and it is shown that the former can be embedded in the latter as a reflective subcategory.
KeywordsFuzzy topology Fuzzy convergence L-prefilter Quasi-coincident neighborhood system Cartesian-closedness Reflective subcategory
The authors would like to express their sincere thanks to the anonymous reviewers and the area editor for their careful reading and constructive comments. The first author thanks to the Natural Science Foundation of China (No. 11701122) and the Natural Science Foundation of Guangdong Province (No. 2017A030310584). The second author thanks to the Scientific Research Foundation of CUIT (KYTZ201631, CRF201611, 17ZB0093).
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Conflict of interest
The authors declare that they have no conflict of interest regarding the publication of this paper.