Functionally Separation Axioms on General Topology - Abdelwaheb Mhemdi; Tareq M. Al-shami (Journal of Mathematics)
In this paper, we define a new family of separation axioms in the classical topology called functionally Ti spaces for i=0,1,2. With the assistant of illustrative examples, we reveal the relationships between them as well as their relationship with Ti spaces for i=0,1,2. We demonstrate that functionally Ti spaces are preserved under product spaces, and they are topological and hereditary properties. Moreover, we show that the class of each one of them represents a transitive relation and obtain some interesting results under some conditions such as discrete and Sierpinski spaces.