Studying deterministic operators, we define an appropriate topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer quantum Hall effect, and lastly we show why our "insulator" condition makes sense from the point of view of the localization theory using the fractional moments method.

中文翻译：

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迁移率间隙绝缘体的拓扑结构

研究确定性算子，我们在迁移率间隙绝缘体的空间上定义了适当的拓扑结构，使得拓扑不变量是连续映射到离散空间，我们证明这确实是整数量子霍尔效应的情况，最后我们展示了为什么我们的“从使用分数矩方法的局部化理论的角度来看，绝缘体”条件是有意义的。