A note on periodic points and transitive maps

A 1999 result of Alseda, Kolyada, Llibre and Snoha states that if X is con- nected and a compact topological space with a disconnecting interval and if f is a transitive map on X, then the set of periodic orbits of f is dense. In this note we show that it is not necessary to assume that X is connected. We also show that the set of all periodic points of a transitive but not totally transitive map on a graph is dense.