We study the space of continuous $Z^d$-actions on the Cantor set,particularly questions on the existence and nature of actions whose isomorphismclass is dense (Rohlin's property). Kechris and Rosendal showed that for $d=1$there is an action on the Cantor set whose isomorphism class is residual. Weprove in contrast that for $\geq 2$ every isomorphism class is meager; on theother hand, while generically an action has dense isomorphism class and theeffective actions are dense, no effective action has dense isomorphism class.Thus for $d \geq 2$ conjugation on the space of actions is topologicallytransitive but one cannot construct a transitive point. Finally, we show thatin the space of transitive and minimal actions the effective actions arenowhere dense, and in particular there are minimal actions that are notapproximable by minimal SFTs.
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机译：我们研究了Cantor集上连续$ Z ^ d $-动作的空间，特别是关于同构类密集的动作的存在性和性质（Rohlin的性质）。 Kechris和Rosendal表明，对于$ d = 1 $，在Cantor集上存在一个动作，该动作的同构类为残差。相反，我们证明对于$ \ geq 2 $，每个同构类都是微不足道的；另一方面，虽然一个动作通常具有密集的同构类，而有效的动作是密集的，但没有有效的动作具有密集的同构类。因此，对于$ d \ geq 2 $，在动作空间上的共轭是拓扑可传递的，但是不能构造一个传递点。最后，我们表明在传递动作和最小动作的空间中，有效动作无处密集，尤其是存在最小动作无法与最小SFT近似的最小动作。
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