Dense

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Revise page, add some links to propositions or theorems using the dense property. Also more references, then demote

Definition

Let $(X,\mathcal{ J })$ be a topological space and let $A\in\mathcal{P}(X)$ be an arbitrary subset of $X$. We say "$A$ is dense in $X$ if:

• $\overline{A}=X$ - that is to say that the closure of $A$ is the entirety of $X$ itself.

See also

• Equivalent statements to a set being dense
  • A set is dense if and only if every non-empty open subset contains a point of it