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Tim Maudlin - New Foundations for Physical Geometry The Theory of Linear Structures [2014][A]

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 							Product Details
  Book Title: New
Foundations for Physical Geometry: The Theory of Linear Structures	 	
  Book Author: Tim Maudlin (Author) 
   Hardcover: 376 pages
   Publisher: Oxford University
Press (May 15, 2014)
   Language: English
   ISBN-10: 0198701306
   ISBN-13: 978-0198701309
  

 Book Description
  Publication Date: May 15,
2014
  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 the Theory of Linear
Structures are laid down, and definitions of other geometrical notions developed in those terms. Various novel
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 noted. The
mathematics is developed up through homotopy theory and compactness, along with ways to represent both affine (straight
line) and metrical structure.
  
  About the
Author
  Tim 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. 						

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