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In a pursuit-evasion game, a team of pursuers attempt to capture an evader.The players alternate turns, move with equal speed, and have full informationabout the state of the game. We consider the most restictive capture condition:a pursuer must become colocated with the evader to win the game. We prove twogeneral results about pursuit-evasion games in topological spaces. First, weshow that one pursuer has a winning strategy in any CAT(0) space under thisrestrictive capture criterion. This complements a result of Alexander, Bishopand Ghrist, who provide a winning strategy for a game with positive captureradius. Second, we consider the game played in a compact domain in Euclideantwo-space with piecewise analytic boundary and arbitrary Euler characteristic.We show that three pursuers always have a winning strategy by extending recentwork of Bhadauria, Klein, Isler and Suri from polygonal environments to ourmore general setting.

Two-Dimensional Pursuit-Evasion in a Compact Domain with Piecewise Analytic Boundary