CHARACTERIZATIONS OF (L;M)-FUZZY TOPOLOGY DEGREES

Authors

  • Fu-Gui Shi 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.
  • Yu Zhong College of Science, North China University of Technology, Beijing, P. R. China
Abstract:

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 $f: Xlongrightarrow Y$ 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.

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Journal title

volume 15  issue 4

pages  129- 149

publication date 2018-08-30

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