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- DescriptionTopology 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 tions 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 tion of standard topology, the open set, with the tion of a continuous line. Axioms for the Theory of Linear Structures are laid down, and definitions of other geometrical tions developed in those terms. Various vel geometrical properties, such as a space being intrinsically directed, are defined using these resources. Applications of the theory to discrete spaces (where the standard theory of open sets gets little purchase) are particularly ted. The mathematics is developed up through homotopy theory and compactness, along with ways to represent both affine (straight line) and metrical structure.
- Author BiographyTim Maudlin was born and raised in Washington DC. Having received his BA in Physics and Philosophy from Yale and his PhD in History and Philosophy of Science from the University of Pittsburgh, he was a faculty member at Rutgers University for a quarter century before joining New York University in 2011. He has been a visiting professor of philosophy at Harvard.
- Author(s)Tim Maudlin
- PublisherOxford University Press
- Date of Publication06/03/2014
- Place of PublicationOxford
- Country of PublicationUnited Kingdom
- ImprintOxford University Press
- Content NoteIllustrations
- Weight720 g
- Width162 mm
- Height240 mm
- Spine31 mm
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