By $C^0$-closing lemma, if $f$ is a continuous map on compact manifold $M$ and $x$ is a non-wandering point, $x\in\Omega(f)$, then for every $\delta>0$, there is $g:M\to M$ with $d_0(f, g)<\delta$ such that $x$ is a periodic point of $g$.
Note that $x\in \Omega(f)$ if for every $\epsilon>0$, there is $n\in\mathbb{N}$ such that $f^n(B_\epsilon(x))\cap B_\epsilon(x)\neq \emptyset$. Also $d_0(f, g)= \sup_{x\in M}d(f(x), g(x))$.
Denote by $CL(f)$ the set of $x\in X$ such that for every $\epsilon>0$ there is a homeomorphism $g:X\to X$ with $d_0(f, g)<\epsilon$, such that $x$ is a periodic point of $g$.
What can say about relation $CL(f)$ and $\Omega(f)$?
Please help me to know it.