Abstract
There are several attempts to generalize (or "widen") the concept of topological space. This paper uses equivalence relations to generalize the concept of topological space via the concept of equivalence relations. By the generalization, we can introduce from particular topology on a nonempty set X many new topologies, we call anyone of these new topologies a dense topology. In addition, we formulate some simple properties of dense topologies and study suitable generalizations of the concepts of limit points, closeness and continuity, as well as Jackson, Norlund and Hahn dense topologies.