Comparison of two types of separation axioms in soft topological spaces1

Abstract

Soft separation axioms and their properties are popular topic in the research of soft topological spaces. Two types of separation axioms Ti-I and Ti-II (i = 0, 1, ⋯ , 4) which take single point soft sets and soft points as separated objects have been given in [18] and [30] respectively. In this paper we show that a soft T0-II(T1-II, T2-II, and T4-II respectively) space is a soft T0-I(T1-I, T2-I, and T4-I respectively) space, if the initial universe set X and the parameter set E are sets of two elements. Some examples are given to explain that a soft Ti-I may not to be a soft Ti-II space (i = 0, 1, ⋯ , 4).