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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 63, Issue 2
  • April 1967, pp. 481-501

On the structure of causal spaces

  • E. H. Kronheimer (a1) and R. Penrose (a1)
  • DOI:
  • Published online: 24 October 2008

The paper examines the structure obtained by abstracting from the conventional (manifold) representation of relativistic space-time the concept of an event-set equipped with two partial orderings, whose counterparts are the notions ‘causally precedes’ and ‘chronologically precedes in the history of some observer’.

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(1)Y. Ahmavaara The structure of space and the formalism of relativistic quantum theory. I. J. Math. Phys. 6 (1965), 8793.

(3)H. S. M. Coxeter and G. J. Whitrow World-structure and non-Euclidean honeycombs. Proc. Roy. Soc. London Ser. A201 (1950), 417437.

(4)D. Finkelstein and C. W. Misner Some new conservation laws. Ann. Physics 6 (1959), 230243.

(5)S. W. Hawking The occurrence of singularities in cosmology. Proc. Roy. Soc. London Ser. A294 (1966), 511521.

(6)E. L. Hill Relativistic theory of discrete momentum space and discrete space-time. Phys. Rev. 100 (1955), 17801783.

(7)C. W. Misner The flatter regions of Newman, Unti, and Tamburino's generalized Schwarzschild space. J. Math. Phys. 4 (1963), 924937.

(8)R. Penrose Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14 (1965), 5759.

(9)R. Penrose Zero rest-mass fields including gravitation: asymptotic behaviour. Proc. Roy. Soc. London Ser. A284 (1965), 159203.

(10)R. Penrose A remarkably property of plane waves in general relativity. Rev. Mod. Phys. 37 (1965), 215220.

(11)A. Schild Discrete space-time and integral Lorentz transformations. Canad. J. Math. 1 (1949), 2947.

(12)H. S. Snyder Quantized space-time. Phys. Rev. 71 (1947), 3841.

(13)E. C. Zeeman Causality implies the Lorentz group. J. Math. Phys. 5 (1964), 490493.

(14)R. W. Bass and L. Witten Remark on cosmological models. Rev. Mod. Phys. 29 (1957), 452453.

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