This chapter is devoted to a preliminary discussion of semipermeable surfaces. (We shall abbreviate this long name by the notation SPS). R. Isaacs was the first to note the extreme relevance of the property of semipermeability to the theory of differential games and devoted much of his monumental work [Isa75] to it. He realized that a surface in the game-set of a pursuit evasion game that separates a capture zone from an escape zone must have the property that each player should be able to prevent the other player from crossing it in the unwanted sense1. Another important contribution was made by P. Bernhard who was first to point out the necessity to impose extra conditions in order to provide for semipermeability at nonsmooth corners of composite semipermeable surfaces.
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