Comments on some results related to soft separation axioms

Abstract

Separation axioms are among the most widespread, significant and motivating concepts via classical topology. They can be utilized to approach problems related to digital topology and to establish more restricted families of topological spaces. This matter applies to them via soft topology as well. Therefore many research studies about soft separation axioms and their properties have been carried out. However, we observe existing some errors over these studies which it can be attributed to the different types of belong and non-belong relations which were defined via the soft set theory, and to the chosen objects of study: are they ordinary points or soft points? Our desire of removing confusions and constructing accurate framework motivates us to do this investigation. Through this paper, we show some alleged findings obtained in Bayramov and Aras (TWMS J Pure Appl Math 9(1):82–93, 2018), Hussain and Ahmad (Hacet J Math Stat 44(3):559–568, 2015), Matejdes (Int J Pure Appl Math 116(1):197–200, 2017), Singh and Noorie (Ann Fuzzy Math Inform 14(5):503–513, 2017) by giving convenient examples and then we formulate the right forms of these findings. In the last section, we demonstrate the relationships among soft $$T_4$$ -spaces introduced in the previous studies and prove that all types of soft $$T_i$$ -spaces are preserved under finitely soft product space in the cases of $$i=0, 1, 2$$ .