Factorization of the Space of Condensers and the Kernel Convergence

The factorization of the space of condensers in a regular connect and locally connect topological space under the equivalence relation generated by the operation of filling of condenser's plates is considered. The kernel convergence for a filtered family of condensers is defined using the notions of the upper topological limit and the filling operation. The relation between the kernel convergence and the convergence in the factor-topology is described. There are also described the filtered families of condensers for which the both types of convergence are equivalent.