We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric measure spaces appropriately, the subset consisting of those with trivial compact quantum automorphism group is of second Baire category. The latter result can be paraphrased as saying that "most" compact metric measure spaces have no (quantum) symmetries; in particular, they also have trivial ordinary (i.e. classical) automorphism group.

中文翻译：

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通用量子度量刚性

我们通过类比有限图的相应概念来介绍紧凑度量空间的相干代数。作为一个应用，我们表明，在适当地对紧度量测空间的同构类集合进行拓扑后，由那些具有平凡紧致量子自同构群的子集组成的子集是第二贝尔类别。后一个结果可以解释为“大多数”紧致度量空间没有（量子）对称性；特别是，它们还具有平凡的普通（即经典）自同构群。