2016/12/24 by Yonatan Gutman, Lei Jin, Gutman, Yonatan +1
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1612.08193
openalex publication_date 2016/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Kakutani-Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of ℝ embeds into the Bebutov flow, the ℝ-shift on C(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.