In the paper, we will prove that if a continuum-wise expansive homeomorphism f of a compact connected metric space X has a local product structure then it has a periodic point. Moreover, if a nontrivial transitive set of a diffeomorphism f of a compact smooth Riemannian manifold M is C1\documentclass[12pt]{minimal}
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\begin{document}$$C^1$$\end{document} stably continuum-wise expansive then it is hyperbolic. These results generalize those of Mañé (Topology 17:383–396, 1978) and Lee and Park (Dyn Syst 33:228–238, 2018).