CHARACTERIZATIONS OF (L;M)-FUZZY TOPOLOGY DEGREES

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.

کلیدواژه ها:

(L ، M)-fuzzy topology degree ، L-open set degree ، Continuity degree ، Openness degree ، Closedness degree ، Quotient degree