Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Orthoalgebras   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

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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph