Computer Implementation of Filters Graph Based on Game Theory

Filter can characterize Moore-Smith convergence theory in general topology. It is different from net, and its properties are more initial. But there is no figure for filters graph on arbitrary set. In this paper, filter, on finite set, is characterized. There is only principle filter on finite set, and it can be determined by its generating set. Then filters graph is defined as graph game. The Sprague-Grundy function of filters graph is analyzed, and each position in filters graph is studied. The condition, which the position is P-position, is show. Finally, sum and product of filters graphs are researched. And by the Sprague-Grundy function, filters graphs, even sum and product, are drawn in some cases.