A general theory of separation, regularity, and connectedness properties

The notion of basic topological binary relations is introduced, and corresponding to each such relation we define -regularity, -connectedness, and a separation axiom . The family of separation axioms so obtained is shown to include all the standard axioms T 0 , T 1 , …, T 5 , while familiar properties such as hyperconnectedness and ultraconnectedness are among the class of connectedness conditions. The regularity conditions include R 0 , R 1 , and regularity itself.