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In this paper, we show that a persistent dynamical system is structurally stable with respect to $E_{\alpha}$(X) for every ${\alpha}$ > 0 if it is expansive. Also, we prove that a homeomorphism$ f:{\Omega}(f){\rightarrow}{\Omega}(f)$ has the semi-shadowing property then so does $f:\overline{C(f)}{\rightarrow}\overline{C(f)}$.
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