No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
A new topology for curved space–time which incorporates the causal, differential, and conformal structures
1.E. C. Zeeman, J. Math. Phys. 5, 490 (1964).
2.E. C. Zeeman, Topology 6, 161 (1967).
3.R. Göbel, Physikal Teil (II) der Habilitationsschrift, Würzburg (1973), and “Zeeman Topologies on Space‐Times of General Relativity Theory,” to appear in Commun. Math. Phys.
4.S. W. Hawking, “Singularities and the Geometry of Space‐Time” (Adams Prize Essay, 1966, unpublished), p. 116.
5.S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space—Time (Cambridge U.P., London, 1973).
6.L. DeFrise‐Carter, Comm. Math. Phys. 40, 273 (1975).
7.Added in proof: We are grateful to Dr. M. Dobson for pointing out that the inverted commas on “times” are essential. The observor does not measure the length of a time interval—many experiments are required to determine whether a set is open.
8.Added in proof: Rüdiger Göbel informed us that he has a modification of the general relativity analog of f which allows the effects of a fixed electromagnetic field to be incorporated. We feel it is preferable to use p, thus allowing all timelike curves to be continuous (not just geodesics or particles with a fixed charge in a fixed field).
9.Added in proof: Actually the Zeeman topology, and Göbel’s generalization admit spacelike curves as continuous curves.
10.Added in proof: We may also assume u to be an open convex normal neighborhood of each of its points.
11.Added in proof: It may also be of interest to note that p is not metrizable, since it is separable but not regular, and neither can p arise from a uniformity, since it is not regular, therefore certainly not completely regular.
Article metrics loading...
Full text loading...