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arXiv · 1412.1645

Enveloping semigroups and quasi-discrete spectrum

Juho Rautio
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Abstract

The structures of the enveloping semigroups of certain elementary finite- and infinite-dimensional distal dynamical systems are given, answering open problems posed by Namioka in 1982. The universal minimal system with (topological) quasi-discrete spectrum is obtained from the infinite-dimensional case. It is proved that, on one hand, a minimal system is a factor of this universal system if and only if its enveloping semigroup has quasi-discrete spectrum and that, on the other hand, such a factor need not have quasi-discrete spectrum in itself. This leads to a natural generalisation of the property of having quasi-discrete spectrum, which is named the $\mathcal{W}$-property.

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Juho Rautio. 2014-12-04. Enveloping semigroups and quasi-discrete spectrum. https://doi.org/10.1017/etds.2015.22

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