Topological Test Spaces

Details Topological Test Spaces Topological Test Spaces

2004-05-28

arxiv.org/abs/quant-ph/0405178v1

Physics

Quantum Physics

12 pp., LaTeX 2e. To appear in Int. J. Theor. Phys

Scientific paper

10.1007/s10773-005-4682-1

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.

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