CHARACTERIZATIONS OF (L;M)-FUZZY TOPOLOGY DEGREES
نویسندگان
1 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China and Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, P.R. China.
2 College of Science, North China University of Technology, Beijing, P. R. China
doi
10.22111/ijfs.2018.4121چکیده
In this paper, characterizations of the degree to which a mapping $\mathcal{T} : L^{X}\longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $\mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: X\longrightarrow Y$ is continuous,open, closed or a quotient mapping with respect to $\mathcal{T}_{X}$ and $\mathcal{T}_{Y}$ are defined, and their characterizations are given, respectively.Besides, the relationships among the continuity degrees, the openness degrees, the closedness degrees and the quotient degrees of mappings are discussed.
