Convergence of sequences of inverse functions

Abstract

The paper deals with a partial solution of the problem: given a conver gence f n - /o of mappings, state conditions under which f" x - f^1.Notation.Let N be the set of natural numbers.Let / : (M, g) - (N, <r), f n : (My g) -> (N, c) denote mappings of a metric space (M, g) into a metric space (N, a) for n N;/ n loc :4/ means that f n converges locally uniformly to / on M as n - oo, i.e. for each x of M, there is a sphere ft(x, r) with centre x and radius r > 0 such that f n converges uniformly to / on Q(x, r) i.e. f n z3 / on 2(x,r).By / -1 we denote the inverse mapping of /, provided / is an injection.Finally, if Mi C M, int Mi and Mi denote the interior of Mi and the closure of Mi, respectively.a?J