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1. Definitions. An admissible space is a finitistic space cf. [B, p. 133] with finitely generated integral homology. Let a group G act on a topological space X, and n: X —• G\X the corresponding projection onto the orbit space. Then S = U^eG-e %* * ̂ e ««gw/ar set and 7r(S) the branch set of the G-action. The G-action is said to be free resp. semifree resp. pseudofree if S = 0 resp. resp. S is d...