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Topology in the Causal Boundary of a Spacetime: (1) Quasi-Compactness in General and (2) Non-Hausdorffness for Simple Product Spacetimes

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Steve Harris, SLU

  • Topology Seminar
When Thu, Sep 07, 2006
from 03:10 PM to 04:00 PM
Where RH 222
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Abstract: (1) Adding the future causal boundary to a strongly causal spacetime results in a topological space with causal structure which has this quasi-compact property: Any sequence of points has a subsequence with a limit point so long as there is an event in the common past of infinitely many of those points. (2) For a simple product spacetime, R x N (N Riemannian), adding the causal boundary produces a result (the causal completion) which is related to a simple product on a compactification of N (formed from adding its Busemann boundary). Either that Busemann compactification is Hausdorff and the causal completion of the spacetime is essentially a simple product of R with the Busemann compactification of N; or the Busemann compactification is non-Hausdorff, requiring more convergence than is naively expected, and the causal completion of the spacetime is more complicated than a product structure.

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