On separation axioms in fuzzifying topology

Abstract

In the present paper we introduce R 0 - and R 1 -separation axioms in fuzzifying topology and study their relations with T 1 - and T 2 -separation axioms, respectively. Furthermore, we introduce and study semi- T 0 -, semi- R 0 -, semi- T 1 -, semi- R 1 -, semi- T 2 (semi-Hausdorff)-, semi- T 3 (semi-regularity)- and semi- T 4 (semi-normality)-separation axioms in fuzzifying topology and give some of their characterizations as well as the relations of these axioms and other separation axioms in fuzzifying topology introduced by Shen, Fuzzy Sets and Systems 57 (1993) 111–123.