Local homeomorphisms having local ACLn inverses

We consider local homeomorphisms between domains from R-n satisfying condition (N) and having local ACL(n) inverses. For such mappings we generalize some basic facts from the theory of quasiregular mappings as the modular inequality of Poleckii and estimates of the modulus of spherical rings from [Koskela, P. and Onninen, J., 2002, Mappings of finite distortion: capacity and modulus inequalities, Preprint 257, University of Jyvaskyla; Martio, O., Ryazanov, V., Srebro, U. and Yakubov, E., 2005, On Q-homeomorphisms, Annales Academiae Scientarum Fennicae Mathematica, 30, 49-69] and [ Martio, O., Ryazanov, V., Srebro, U. and Yakubov, E., 2002, Mappings of finite length distortion, Preprint 322, Reports Mathematics Department, University of Helsinki], and we use these facts to extend Zoric's theorem and to calculate the radius of injectivity for this class of mappings.