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Here is a systematic approach to such fundamental questions as: What mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The author proposes an axiomatization of the physics inspired notion of Einstein-Weyl causality and investigating the consequences in terms of possible topological spaces. One significant result is that the notion of causality can effectively be extended to discontinuum.
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The present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The authors propose an axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one that is locally a differentiable manifold. The mathematical level required of the reader is that of the graduate student in mathematical physics.Review:
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"The casual structure of space-times can be described by means of two notions of precedence, namely chronological and casual precedence; one can then abstract these two notions, and the relationship between them, and consider casual spaces in general. ... This volume will be of interest in particular to workers in casual analysis, and more generally to those with an interest in the fundamental structure of space-time." (Robert J. Low, Mathematical Reviews, 2007 k)
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