Topologies for Lorentz manifolds: the space topology.

Details Topologies for Lorentz manifolds: the space topology. Topologies for Lorentz manifolds: the space topology.

Dec 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985gregr..17.1165d&link_type=abstract

General Relativity and Gravitation, Volume 17, Issue 12, pp.1165-1176

Computer Science

Gravitation Theory:Metrics

Scientific paper

The main result in this note states and proves that the space topology for Lorentz manifolds is 0-semimetrizable. This is in a certain sense the “spacelike” version of an analogous result for the Hawking-King-McCarthy path topology, which was published in [5]. But the proofs are completely different. The space topology is the finest topology on a Lorentz manifold, which induces the manifold topology on every spacelike hypersurface. Its geometric significance comes from the fact, that its full homeomorphismgroup is the group of all conformal diffeomorphisms. 0-semimetrics are very natural generalizations of metrics and have interesting interpretations as “statistical metrics” and as “metrics with an elementary length.”

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