General Relativity and Gravitation

, Volume 8, Issue 4, pp 245–257 | Cite as

A metric topology for causally continuous completions

  • John K. Beem
Research Articles

Abstract

A metric topologyH(¯M) is introduced on the causal completion¯M of a causally continuous space-timeM. This metric topology is at least as coarse as the extended Alexandrov topologyA(¯M) on¯M. In bothH(¯M) andA(¯M), the original space-timeM is an open and dense subset. From the definition ofH(¯M), it follows that the causality on¯M is continuous at boundary points. IfM admits a compact Cauchy surface, thenH(¯M) andA(¯M) are the same.

Keywords

Boundary Point Differential Geometry Dense Subset Cauchy Surface Compact Cauchy Surface 

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Copyright information

© Plenum 1977

Authors and Affiliations

  • John K. Beem
    • 1
  1. 1.Department of MathematicsUniversity of MissouriColumbia

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