Spacetime Topology
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High Quality Content by WIKIPEDIA articles! Spacetime topology, the topological structure of spacetime, is a subject studied primarily in general relativity. This physical theory models gravitation as a Lorentzian manifold (a spacetime) and the concepts of topology thus become important in analysing local as well as global aspects of spacetime. The study of spacetime topology is especially important in physical cosmology. As with any manifold, a spacetime possesses a natural manifold topology. Here the open sets are the image of open sets in mathbb{R}^n. The Alexandrov topology, also called…mehr

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High Quality Content by WIKIPEDIA articles! Spacetime topology, the topological structure of spacetime, is a subject studied primarily in general relativity. This physical theory models gravitation as a Lorentzian manifold (a spacetime) and the concepts of topology thus become important in analysing local as well as global aspects of spacetime. The study of spacetime topology is especially important in physical cosmology. As with any manifold, a spacetime possesses a natural manifold topology. Here the open sets are the image of open sets in mathbb{R}^n. The Alexandrov topology, also called the interval topology, is defined in terms of the causality relations in the spacetime. It is the coarsest topology such that I + (E) is open for all subsets E subset M. Here the base of open sets for the topology are sets of the form I^+(x) cap I^-(y) for some points ,x,y in M. This topology coincides with the manifold topology iff the manifold is strongly causal but in general it is coarser.