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arXiv · 1612.08193

An explicit compact universal space for real flows

Yonatan Gutman·Lei Jin
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Abstract

The Kakutani-Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.

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Yonatan Gutman, Lei Jin. 2016-12-24. An explicit compact universal space for real flows. https://arxiv.org/abs/1612.08193

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