It is proved that for any C~1 self-covering map f of a compact connected Riemann manifoldwithout boundary, if f satisfies both axiom A and the no-cycle property, and Ω(f) has (s-c-u.)structure, then the structure of its orbit space is topologically stable (semi-stable) underC~0 perturbation and structurally stable under C~1 perturbation. It seems very difficult to theauthors to extend the results of Robbinson and Nitecki to the case of self-maps. Such exten-sions were expected to be solved by Z. Nitecki. This paper may be regarded as a step for-ward in this direction.
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