  We study mappings defined in the domain of a metric space that distort the
modulus of families of paths by the type of the inverse Poletskii inequality.
Under certain conditions, it is proved that such mappings have a continuous
extension to the boundary of the domain in terms of prime ends. Under some
additional conditions, the families of such mappings are equicontinuous in the
closure of the domain with respect to the space of prime ends.
