New Foundations for Physical Geometry: The Theory of Linear Structures

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Topology is the mathematical study of the most basic geometrical structure of a space. Mathematical physics uses topological spaces as the formal means for describing physical space and time. This book proposes a completely new mathematical structure for describing geometrical notions such as continuity, connectedness, boundaries of sets, and so on, in order to provide a better mathematical tool for understanding space-time. This is the initial volume in a two-volume set, the first of which develops the mathematical structure and the second of which applies it to classical and Relativistic physics. The book begins with a brief historical review of the development of mathematics as it relates to geometry, and an overview of standard topology. The new theory, the Theory of Linear Structures, is presented and compared to standard topology. The Theory of Linear Structures replaces the foundational notion of standard topology, the open set, with the notion of a continuous line. Axioms for

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Author : Tim Maudlin

Pages : 376 pages

Publisher : Oxford University Press, USA

Language :

ISBN-10 : 0198701306

ISBN-13 : 9780198701309

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New Foundations for Physical Geometry: The Theory of Linear Structures

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