recurrent point of

Let a continuum X and a mapping $f: X \to X$ be given. For each natural number n denote by fⁿ the n-th iteration of f. A point $p \in X$ is called a recurrent point of f provided that for every neighborhood U of p there is $n \in \mathbb{N}$ such that $f^n(p) \in U$. The set of recurrent points of a mapping $f: X \to X$ are denoted by R(f).