periodic-recurrent property

The set of periodic points and of recurrent points of a mapping $f: X \to X$ are denoted by P(f) and R(f) respectively. Clearly $P(f) \subset R(f)$. A continuum X is said to have the periodic-recurrent property (shortly PR-property) provided that for every mapping $f: X \to X$ the equality $\mathrm{cl}\,P(f) = \mathrm{cl}\,R(f)$ holds.