Functionally separation axioms on general topology
Summary: 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.
scientific article; zbMATH DE number 7363831