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. Introduction....Pages 1-6 Geometrical Structures on Space-Time....Pages 7-14 Light Rays and Light Cones....Pages 15-30 Local Structure and Topology....Pages 31-50 Homogeneity Properties....Pages 51-65 Ordered Spaces and Complete Uniformizability....Pages 67-94 Spaces with Complete Light Rays....Pages 95-101 Consequences of Order Completeness....Pages 103-127 The Cushion Problem....Pages 129-135 Related Works....Pages 137-146 Concluding Remarks....Pages 147-156 Erratum to: Geometrical Structures on Space-Time....Pages 191-191 Erratum to: Light Rays and Light Cones....Pages 191-191 Erratum to: Local Structure and Topology....Pages 191-192 Erratum to: Ordered Spaces and Complete Uniformizability....Pages 192-192 Erratum to: Spaces with Complete Light Rays....Pages 192-192 Erratum to: Consequences of Order Completeness....Pages 192-192 Erratum....Pages 192-192 "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 Title from e-book title screen (viewed June 27, 2008).