论文标题
群体模棱两可的非强化操作员的感知对和空间的压缩
Compactification of Perception Pairs and Spaces of Group Equivariant non-Expansive Operators
论文作者
论文摘要
我们定义了紧凑的感知对的概念，感知对的紧凑化以及集体均等非扩展算子的空间的压实。我们证明，每个具有完全有限的测量空间的感知对，也足够丰富，可以将公共域具有度量结构赋予，可以嵌入紧凑的感知对中。同样，我们证明，如果在给定空间中的小组非表达运算符的图像构成了它们的共同代码域的覆盖，那么该操作员的空间可以均匀地嵌入到集团的非表达运算符的紧凑型空间中，因此新的参考感知对具有完全有限数据的原始数据集的新型参考感是压实的。同时，我们陈述了这些嵌入的一些兼容条件，并表明它们也对我们的构造感到满意。
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.
