The Relations between Characterized Fuzzy Proximity, Fuzzy Compact, Fuzzy Uniform Spaces and Characterized Fuzzy Ts–Spaces and Fuzzy Rk–Spaces

[摘要] In this research work, we study the relations between the characterized fuzzy Ts–spaces and characterized fuzzy Rk–spaces presented in old papers, for s ∈ {0,1,2,3,3 1/2 ,4} and  k ∈ {1,2,2 1/2 ,3} and the characterized fuzzy proximity spaces presented. We also study the relations between the characterized fuzzy Ts–spaces, the characterized fuzzy Rk–spaces and the characterized fuzzy compact spaces which is presented in old paper, as a generalization of the weaker and stronger forms of the G–compactness defined by Gähler. Moreover, we show here the relations between these characterized fuzzy Ts–spaces, characterized fuzzy Rk–spaces and the characterized fuzzy uniform spaces introduced and studied by Abd-Allah in 2013 as a generalization of the weaker and stronger forms of the fuzzy uniform spaces introduced by Gähler.

[关键词] Fuzzy filter;Fuzzy topological space;Operationsl;Isotone and idempotent;Characterized fuzzy space;φ1;2–fuzzy neighborhood filters;Fuzzy uniform structure;Characterized fuzzy proximity space;Characterized fuzzy compact space;Characterized fuzzy uniform space;Characterized FTs–space;Fφ1;2–Ts space;Characterized FRk–space and Fφ1;2–Rk space for