If D is dense in a topological space X tau prove that D is d

If D is dense in a topological space (X, tau), prove that D is dense in every topology smaller than tau.

Solution

If (X,T) is atopological space, then X is the set and T is the topology on X.T is also the family of subsets of X.

If an element in the set X, D refers to \'dense\', then, an element D in T refers to dense only. A subset can derive elements only from its superset.