Given a continuous open finite-to-one mapping $ f $ of a domain $ G $ including a closed set $ E $ ,for each natural $ k $ we consider the set $ E(k) $ (possibly empty)of all points in $ E $ at which $ f $ attains a value with multiplicity $ k $ over $ G $ .Suppose thateach point of $ E(k) $ has a neighborhoodwhere the restriction of $ f $ to $ E(k) $ is injective,and its inverse mapping is weakly $ (h,H) $ -quasisymmetric.If, moreover, $ f $ is quasiregular outside $ E $ ,then it is quasiregular on the entire domain $ G $ .This theorem generalizesthe sufficient condition for the removability of closed setsin the class of quasiconformal mappingsobtained by Väisälä in 1990.
