In this work we provide the full description of the upper levels of the classical causal ladder for spacetimes in the context of Lorenztian length spaces, thus establishing the hierarchy between them. We also show that global hyperbolicity, causal simplicity, causal continuity, stable causality and strong causality are preserved under distance homothetic maps.
Abstract. This note proves the geodesic completeness of any compact manifold endowed with a linear connection such that the closure of its holonomy group is compact.
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