The filling of condensers and kernel-type convergence

The kernel convergence of sequences of condensers in a connected and locally connected metric space is investigated in this paper. This type of convergence has been introduced here with using the topological operation of filling. The general theorem states that the continuity of a condenser’s characteristic under the topological convergence is tranferred to the case of kernel convergent sequences of condensers. In particularly, the continuity of conformal capacity is proved for the kernel-convergent sequences of condensers with uniformly perfect plates.