A new topology is proposed for strongly causal space–times. Unlike the standard manifold topology (which merely characterizes continuity properties), the new topology determines the causal, differential, and conformal structures of space–time. The topology is more appealing, physical, and manageable than the topology previously proposed by Zeeman for Minkowski space. It thus seems that many calculations involving the above structures may be made purely topological.

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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.
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