D-countability axioms

In this paper, we introduce new axioms using the concepts of the countability axioms via dense sets, namely dense countability axioms and they are denoted by D-countability axioms, where a topological space is called D-sequential (D-separable, D-first countable, D-Lindelöf, D--compact or D-second countable) space if it has a dense sequential (separable, first countable, Lindelöf, -compact or second countable) subspace. We prove that D-separable spaces and D-second countable spaces are equivalent to separable spaces. Moreover, we study some properties of D-countability axioms; as their subspaces and their continuous images. In addition, we provide some inter-relations between D-countability axioms and countability axioms through some examples.