Abstract
The purpose of this paper is to introduce a new type of separation axioms via dense sets, called DTi -spaces (i = 0‚1 4 ‚ 1 3 ‚ 1 2 ‚ 3 4 ‚1), where a DTi -space is a topological space which contains a dense Ti - subspace (i = 0‚1 4 ‚ 1 3 ‚ 1 2 ‚ 3 4 ‚1). These new axioms are weaker than the axiom of T1 . We provide the basic properties of DTi - spaces (i = 0‚1 4 ‚ 1 3 ‚ 1 2 ‚ 3 4 ‚1), and we show that the axioms of DT1 4 , DT1 3 , DT1 2 , DT3 4 , DT1 are open hereditary. Moreover, we study the connections between these axioms and the axioms of Ti where (i = 0‚ 1 4 ‚ 1 3 ‚ 1 2 ‚ 3 4 ‚1).