  We study mappings that satisfy the inverse modulus inequality of Poletsky
type in a fixed domain. It is shown that, under some additional restrictions,
the image of a ball under such mappings contains a fixed ball uniformly over
the class. This statement can be interpreted as the well-known analogue of
Koebe's theorem for analytic functions. As an application of the obtained
result, we show that, if a sequence of mappings belonging to the specified
class converges locally uniformly, then the limit mapping is open.
