Let $(X, \mathcal{U})$ be a uniform space and $f:X\to X$ be a homeomorphism. For symmetric element $A\in\mathcal{U}$, let $A(f)$ be the set of all homeomorphisms $g:X\to X$ such that $(g(x), f(x))\in A$ for all $x\in X$.
The point $x\in X$ is a non-wandering point of $f$, $x\in\Omega(f)$, if for all $D\in \mathcal{U}$ there is $n\in\mathbb{N}$ such that $f^n(D[x])\cap D[x]\neq \emptyset$.
Let $\mathcal{N}(f)$ be the set $x\in X$ such that for every $A\in \mathcal{U}$, there is $g\in A(f)$ such that $x\in Per(g)$.
What is the relation between $\mathcal{N}(f)$ and $\Omega(f)$?