We determine the reflexivity index of some closed set lattices by constructing maps relative to irrational rotations. For example, various nests of closed balls and some topological spaces, such as even-dimensional spheres and a wedge of two circles, have reflexivity index 2. We also show that a connected double of spheres has reflexivity index at most 2.

中文翻译：

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自反性指数和无理旋转

我们通过构建相对于非理性旋转的映射来确定一些闭集格的自反指数。例如，封闭球的各种嵌套和一些拓扑空间，例如偶数维球体和两个圆的楔形，具有自反指数 2。我们还证明了一个连通的双球体的自反指数最多为 2。