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    Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes

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    The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime (M,g)(M,g) admits a smooth time function τ\tau whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting M=R×SM= \R \times {\cal S}, g=−β(τ,x)dτ2+gˉτg= - \beta(\tau,x) d\tau^2 + \bar g_\tau , (b) if a spacetime MM admits a (continuous) time function tt (i.e., it is stably causal) then it admits a smooth (time) function τ\tau with timelike gradient ∇τ\nabla \tau on all MM.Comment: 9 pages, Latex, to appear in Commun. Math. Phys. Some comments on time functions and stably causal spacetimes are incorporated, and referred to gr-qc/0411143 for further detail

    Backward Φ-shifts and universality

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    In this paper we consider spaces of sequences which are valued in a topological space E and study generalized backward shifts associated to certain selfmappings of E. We characterize their universality in terms of dynamical properties of the underlying selfmappings. Applications to hypercyclicity theory are given. In particular, Rolewicz’s theorem on hypercyclicity of scalar multiples of the classical backward shift is extended.Plan Andaluz de Investigación (Junta de Andalucía
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