拓扑检验空间
Topological Test Spaces
摘要：
测试空间是与实验集合相关联的结果集的集合。这一概念为概率理论的研究提供了一个简单的数学框架--特别是量子力学--在量子力学中，人们面对的是不可解释的随机量。在量子力学的情况下，相关的测试空间，希尔伯特空间的标准正交基的集合，具有重要的拓扑结构。本文开创了拓扑检验空间的一般性研究。除其他外，我们表明，任何拓扑测试空间与一个紧凑的空间的结果是有限的秩。我们还推广了Meyer和Clifton-Kent的结果，证明了在非常弱的假设下，任何第二可数拓扑检验空间都包含一个稠密的半经典检验空间。
英文摘要：
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with incommensurable random quantities. In the case of quantum mechanics, the relevant test space, the set of orthonormal bases of a Hilbert space, carries significant topological structure. This paper inaugurates a general study of topological test spaces. Among other things, we show that any topological test space with a compact space of outcomes is of finite rank. We also generalize results of Meyer and Clifton-Kent by showing that, under very weak assumptions, any second-countable topological test space contains a dense semi-classical test space.
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。
