The class of continuous timelike curves determines the topology of spacetime
1.E. H. Kronheimer and R. Penrose, Proc. Camb. Phil. Soc. 63, 481 (1967).
2.S. W. Hawking, A. R. King, and P. J. McCarthy, J. Math. Phys. 17, 174 (1976).
3.Proofs of these and subsequent claims can be found in S. W. Hawking and G. F. R. Ellis. The Large Scale Structure of Spacetime (Cambridge U.P., Cambridge, 1973);
3.R. Penrose, Techniques of Differential Topology in Relativity (SIAM, Philadelphia, 1972).
4.A proof is given in Hawking, King, and McCarthy (Ref. 2). The theorem is not formulated in exactly this from, but the argument carries over intact.
5.This version of the theorem is applicable to all temporally orientable spacetimes whether or not a particular temporal orientation is distinguished.
6.Hawking and Ellis (Ref. 3) prove this in detail in their Lemma 6.2.1.
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