The Kakutani-Bebutov Theorem (1968) says that if a compact
metric real flow satisfies that the set of its fixed points is
homeomorphic to a subset of the real line, then it is embeddable into
the shift on the space of all continuous functions from the real line to
the unit interval. An interesting fact is that this universal space is a
function space; however, it is not compact, nor locally compact. We
provide an explicit compact metric universal space for all compact
metric real flows, with no restriction, which is a countable product of
compact function spaces; namely, we construct a compact metric real flow
into which we can embed all compact metric real flows.
This is a joint work with Yonatan Gutman (2016).