-Spaces in Smooth Topological Spaces
نویسندگان
چکیده
ـــــ In [25], we introduce the notion of r-fuzzy neighborhood filters in smooth topological spaces in sense of Gähler [10], and used it to define and study separation axioms , = , , . Here we continue our study of the axioms of separation in smooth topological spaces. Therefore, we introduce the notion of r-fuzzy neighborhood filter at a set. Then by using this notion we define and study separation axioms , = , . These axioms are related only to usual points and ordinary subsets and reduce to axioms defined in [5], if : → { , }. So the current separation axioms are generalization of the old one. In addition, we show -space not necessarily be a -space for i=3,4. We give a condition for which, -space is a -space for i=3,4. Finally, these axioms are good extension from the point of view of Aygün et al. [2]. Keywordsـــ Smooth topological space, fuzzy filter, r-fuzzy neighborhood filter, regular space, normal space. Mathematics Subject Classification: 54A05, 54A40, 54E55, 54C08
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