Factorization of the Space of Condensers and the Kernel Convergence

V. V. Aseev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: 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.

UDC: 515.12:517.54

Received: 01.11.2006