In this paper, we define a new family of separation axioms in the classical topology called functionally
T
i
spaces for
i
=
0,1,2
. With the assistant of illustrative examples, we reveal the relationships between them as well as their relationship with
T
i
spaces for
i
=
0,1,2
. We demonstrate that functionally
T
i
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.
Hereditary properties of product spaces
