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A Non-commutative Monotone Selection Principle

Marco Thill
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Abstract

We give an elementary proof of a monotone selection principle which allows to pass from increasing nets to increasing sequences in the Hermitian part of a $σ$-finite von Neumann algebra. This is to be seen as a ``monotone version'' of first countability.

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Marco Thill. 2003-12-02. A Non-commutative Monotone Selection Principle. https://arxiv.org/abs/math/0312061

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