This paper, deals with, introduce and study the notions of haracterized fuzzy R2.5spaces and of characterized fuzzy T3.5spaces by using the notion of fuzzy function family presentedin [21] and the notion of φ1,2ψ1,2-fuzzy continuous mappings presented in [5] as a generalization ofall the weaker and stronger forms of the fuzzy completely regular spaces introduced in [11,24,26,29].We denote by characterized fuzzy T3.5 space or characterized fuzzy Tychonoff space to the characterizedfuzzy space which is characterized fuzzy T1 and characterized fuzzy R2.5space in thissense. The relations between the characterized fuzzy T3.5spaces, the characterized fuzzy T4 spaces and the characterized fuzzy T3 spaces are introduced. When the given fuzzy topological space isnormal, then the related characterized fuzzy space is finer than the associated characterized fuzzyproximity space which is presented in [1]. Moreover, the associated characterized fuzzy proximityspaces and the characterized fuzzy T4 spaces are identical with help of the complementarilysymmetric fuzzy topogenous structure, that is, identified with the fuzzy proximity δ. More generally,the fuzzy function family of all φ1,2ψ1,2-fuzzy continuous mappings are applied to show thatthe characterized fuzzy R2.5 spaces and the associated characterized fuzzy proximity spaces areidentical.
Characterized Fuzzy R2.5 and Characterized Fuzzy T3.5 Spaces
30.03.2017
doi:10.24297/jam.v13i1.5684
JOURNAL OF ADVANCES IN MATHEMATICS; Vol. 13 No. 1 (2017); 7048-7073 ; 2347-1921
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
fuzzy topogenous order , fuzzy proximity , operations , characterized fuzzy R2 , fuzzy filter , fuzzy topological space , 2010AMS classication , 2δ-fuzzy neighborhood , Primary 54E05 , φ1 , fuzzy topogenous structure , 54A15 , 54E15 , characterized fuzzy proximity space , Secondary 54A40 , characterized fuzzy space , fuzzy function family
DDC: | 629 |