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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.
next up previous contents index
Next: pointwise self-homeomorphic Up: Definitions Previous: periodic point of
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30