Characterized Fuzzy R2.5 and Characterized Fuzzy T3.5 Spaces




fuzzy filter, fuzzy topological space, fuzzy proximity, fuzzy topogenous structure, operations, characterized fuzzy space, φ1, 2δ-fuzzy neighborhood, fuzzy topogenous order, fuzzy function family, characterized fuzzy proximity space, characterized fuzzy R2


This paper, deals with, introduce and study the notions of haracterized fuzzy R2.5 spaces and of characterized fuzzy T3.5 spaces by using the notion of fuzzy function family presented in [21] and the notion of φ1,2ψ1,2-fuzzy continuous mappings presented in [5] as a generalization of all 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 characterized fuzzy space which is characterized fuzzy T1 and characterized fuzzy R2.5 space in this sense. The relations between the characterized fuzzy T3.5 spaces, the characterized fuzzy T4 spaces and the characterized fuzzy T3 spaces are introduced. When the given fuzzy topological space is normal, then the related characterized fuzzy space is finer than the associated characterized fuzzy proximity space which is presented in [1]. Moreover, the associated characterized fuzzy proximity spaces 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 that the characterized fuzzy R2.5 spaces and the associated characterized fuzzy proximity spaces are identical.


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Author Biography

Ahmed Saeed Abd-Allah, Department of Mathematics - College of Science - Prince Sattam Bin Abdulaziz University - Saudi Arabia.

Mathematics Department - Professor




How to Cite

Abd-Allah, A. S. (2017). Characterized Fuzzy R2.5 and Characterized Fuzzy T3.5 Spaces. JOURNAL OF ADVANCES IN MATHEMATICS, 13(1), 7048–7073.