A simple proof for a theorem of Luxemburg and Zaanen (Q2506457)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple proof for a theorem of Luxemburg and Zaanen |
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A simple proof for a theorem of Luxemburg and Zaanen (English)
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28 September 2006
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A well-known theorem of Luxemburg and Zaanen states that an Archimedean vector lattice \(E\) is Dedekind \(\sigma\)-complete iff it has the principal projection property and is uniformly complete. A simple proof of this theorem is given here. As an application, a new and short proof of a version of Freudenthal's spectral theorem is given.
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basically disconnected
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Dedekind \(\sigma\)-complete vector lattice
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principal projection property
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