Dense subset

Let $(X, \tau)$ - a topological-space.

A subset $A \subset X$ is called dense in $X$ if $$ \forall x \in X:,\forall U(x) \in \tau \hookrightarrow A \cap U(x) \neq \varnothing $$

Non-dense subset

A subset $A \subset X$ is not dense if

• for metric-space: $[S]{\tau}$ has not any open-ball (i.e. $\operatorname{Int}([S]{\tau}) = \varnothing$)