TY  - JOUR
TT  - Causally Simple Spacetimes and Domain Theory
AU  - Ebrahimi, Neda
PY  - 2014
DA  - November
JF  - Cankaya University Journal of Science and Engineering
JO  - CUJSE
PB  - Cankaya University
WT  - DergiPark
SN  - 2564-7954
VL  - 11
IS  - 2
KW  - Domain theory
KW  - causality
KW  - spacetime
KW  - causally simple
KW  - Alexandrov topology
N2  - Globally, hyperbolic spacetimes are the simplest kind of spacetimes which are studied in GeneralRelativity. It is shown by Martin and Panangaden that it is possible to reconstruct globally hyperbolic spacetimesin a purely order theoretic manner using the causal relation J+. Indeed these spacetimes belong to acategory that is equivalent to a special category of domains known as interval domains [8]. In this paper, it isshown that this result is true for a larger superclass of spacetimes.
CR  - [1] S. Abramsky, A. Jung, Domain theory, Handbook of Logic in Computer Science, S. Abramsky, D. M. Gabbay,
T. S. E. Maibaum (Editors), Volume III, Oxford University Press (1994).
CR  - [2] J. K. Beem, P. E. Ehrlich, K. L. Easley, Global Lorentzian Geometry, Marcel Dekker, New York, (1996).
CR  - [3] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, 2nd Edition, Cambridge University Press, (2002).
CR  - [4] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lowson, M. Mislove, D. S. Scott, Continuous Lattices and Domains,
Encyclopedia Math. Appl. 93, Cambridge University Press, (2003).
CR  - [5] S. W. Hawking and G. F. R. Ellis, The large scale structure of spacetime, Cambridge Monographs on Mathematical
Physics, Cambridge University Press, (1972).
CR  - [6] K. Keimel, Bicontinuous Domains and some old problems in Domain theory, Electron. Notes Theor. Comput. Sci.,
257, (2009), 35–54.
CR  - [7] K. Martin, P. Panangaden, Spacetime topology from causality, Arxiv gr-qc/0407093v1, (2004).
CR  - [8] K. Martin, P. Panangaden, ‘A domain of spacetime intervals in General Relativity”, Commun. Math. Phys. 267,
(2006), 563–586.
CR  - [9] R. Penrose, Techniques of differential topology in Relativity, AMS Colloquium Publications, SIAM Philadelphia,
(1972).
CR  - [10] D. Scott, Outline of a mathematical theory of computation, Technical Monograph PRG-2, Oxford University
Computing Laboratory, (1970).
CR  - [11] Alex Simoson, Part III: Topological Spaces from a Computational Perspective, Mathematical Structures for Semantics, (2001-2002).
CR  - [12] R. M. Wald, General Relativity, University of Chicago Press, (1984).
UR  - https://dergipark.org.tr/en/pub/cankujse/issue//368683
L1  - https://dergipark.org.tr/en/download/article-file/386835
ER  -