Filters on the Cartesian product of two sets (in Russian)

In this paper two constructions on filters are defined and studied --- the so called star-operation and the extension filters which are given on two sets to the direct product of this sets. The necessity of these constructions arises in investigation of topological spaces of formal sums. Applications of the results are also in this area. The main statement is Theorem 28 in which connection between two constructions is established.