On the Continuity of Inverse Mappings for Lipschitz Perturbations of Covering Mappings

In this paper, we study the question of the existence of a continuous right inverse mapping for a covering mapping. To describe covering mappings that have a continuous right inverse, a concept of strong covering is introduced. It is shown that the property of strong covering is stable under small Lipschitz perturbations. Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 19, No. 4, pp. 93–99, 2014. © 2016, Springer Science+Business Media New York.