ИГРА «ЛЕВ И ЧЕЛОВЕК» НА МЕТРИЧЕСКОМ КОМПАКТЕ

The lion and man game on a compact metric space is considered. Both players have the equal speeds. Suppose that 1) for all pairs of points there exists a unique geodesic connecting this points; 2) every geodesic continuously depends on its own endpoints. Then the strategy of simple pursuit guarantees the ε -capture. In particular, this implies the same result for CAT(0) domains.