An explicit compact universal space for real flows |
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Authors: | Yonatan Gutman Lei Jin |
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Affiliation: | Institute of Mathematics, Polish Academy of Sciences, ul. ?niadeckich 8, 00-656 Warszawa, Poland |
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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 embeds into the Bebutov flow, the -shift on . 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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Keywords: | 37B05 54H20 Bebutov–Kakutani theorem Compact metric flow Bebutov flow Bernstein space Universal space Equivariant embedding |
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