From wikipedia simple definition of dense set defined as ,In topology and related areas of mathematics, A subset A of a topological space X is called dense in X if every point x in X either belongs to A or is a limit point of A; that is, the closure of A is constituting the whole set X , the notion of density is widely useful in probability and physics and all branche of mathematics particulary Topology and functional analysis , Now my question here is : What claims and what theorem we can prove in topology and functional analysis using density property and why it's important ?
What claims and what Theorem we can prove using density property in Topology ?