A point $p$ in a topological space $X$ is said to be generic if $\overline{\{p\}} =X$ (i.e. $\{p\}$ is dense in $X$).
Let $G(X)=\{p \mid p\text{ is generic in }X\}$. That is, $G(X)$ is the set of all the points dense in $X$.
$X$ path-connected if $G(X)$ is nonempty.
Show $G(X)$ is a compact subspace of $X$.