感知对的紧化与群等变非扩张算子空间
Compactification of Perception Pairs and Spaces of Group Equivariant non-Expansive Operators
摘要：
我们定义的概念，一个紧凑的感知对，紧化的感知对，紧化的空间组等变非扩张运营商。我们证明了每一个感知对与测量的完全有界空间，这也是足够丰富的，赋予共同的域与度量结构，可以等距嵌入在一个紧凑的感知对。同样，我们证明了，如果在一个给定的空间群等变非扩张算子的图像形成一个覆盖其共同的上域，然后这种操作的空间可以等距嵌入在一个紧空间的群等变非扩张算子，使新的参考感知对是紧化的原始的具有完全有界的数据集。同时，我们陈述了这些嵌入的相容性条件，并证明了我们的构造也满足这些相容性条件。
英文摘要：
We define the notions of a compact perception pair, compactification of a perception pair, and compactification of a space of group equivariant non-expansive operators. We prove that every perception pair with totally bounded space of measurements, which is also rich enough to endow the common domain with a metric structure, can be isometrically embedded in a compact perception pair. Likewise, we prove that if the images of group equivariant non-expansive operators in a given space form a cover for their common codomain, then the space of such operators can be isometrically embedded in a compact space of group equivariant non-expansive operators, such that the new reference perception pairs are compactifications of the original ones having totally bounded data sets. Meanwhile, we state some compatibility conditions for these embeddings and show that they too are satisfied by our constructions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
