Topological Orthoalgebras
摘要
We define topological orthoalgebras (TOAs) and study their properties. While every topological orthomodular lattice is a TOA, the lattice of projections of a Hilbert space is an example of a lattice-ordered TOA that is not a toplogical lattice. On the other hand, we show that every compact Boolean TOA is a topological Boolean algebra. We also show that a compact TOA in which 0 is an isolated point is atomic and of finite height. We identify and study a particularly tractable class of TOAs, which we call {\em stably ordered}: those in which the upper-set generated by an open set is open. This includes all topological OMLs, and also the projection lattices of Hilbert spaces. Finally, we obtain a topological version of the Foulis-Randall representation theory for stably ordered TOAs
引用
@article{arxiv.math/0301072,
title = {Topological Orthoalgebras},
author = {Alexander Wilce},
journal= {arXiv preprint arXiv:math/0301072},
year = {2009}
}
备注
16 pp, LaTex. Minor changes and corrections in sections 1; more substantial corrections in section 5