Continuous Maps of the Interval with Finite Nonwandering Set

Let f be a continuous map of a closed interval into itself, and let $\Omega (f)$ denote the nonwandering set of f. It is shown that if $\Omega (f)$ is finite, then $\Omega (f)$ is the set of periodic points of f. Also, an example is given of a continuous map g, of a compact, connected, metrizable, one-dimensional space, for which $\Omega (g)$ consists of exactly two points, one of which is not periodic.