Mathematical Implications of Einstein-Weyl Causality (Lecture Notes in Physics)

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.--book Jacket. Introduction -- Geometrical Structures On Space-time -- Light Rays And Light Cones -- Local Structure And Topology -- Homogeneity Properties -- Order And Uniformizability -- Spaces With Complete Light Rays -- Consequences Of Order Completeness -- The Cushion Problem -- Related Works -- Concluding Remarks -- [appendices]: A. Uniformities And Uniform Completion -- B. Fibre Bundles And G-structures -- C. The Axioms And Special Assumptions. Hans-jürgen Borchers, Rathindra Nath Sen. Includes Bibliographical References (p. [179]-189) And Index. "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."--Résumé de l'éditeur 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. Title from e-book title screen (viewed June 27, 2008).