New Foundations for Physical Geometry: The Theory of Linear Structures

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9780198701309: New Foundations for Physical Geometry: The Theory of Linear Structures
Reseña del editor:

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.

Biografía del autor:

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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Tim Maudlin
Editorial: Oxford University Press, United Kingdom (2014)
ISBN 10: 0198701306 ISBN 13: 9780198701309
Nuevos Tapa dura Cantidad: 10
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The Book Depository
(London, Reino Unido)
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Descripción Oxford University Press, United Kingdom, 2014. Hardback. Estado de conservación: New. 236 x 160 mm. Language: English . Brand New Book. 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. Nº de ref. de la librería AOP9780198701309

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Tim Maudlin
Editorial: Oxford University Press, United Kingdom (2014)
ISBN 10: 0198701306 ISBN 13: 9780198701309
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Descripción Oxford University Press, United Kingdom, 2014. Hardback. Estado de conservación: New. 236 x 160 mm. Language: English . Brand New Book. 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. Nº de ref. de la librería AOP9780198701309

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Tim Maudlin
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Descripción OUP Oxford 2014-03-06, Oxford, 2014. hardback. Estado de conservación: New. Nº de ref. de la librería 9780198701309

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Descripción Oxford University Press. Estado de conservación: New. Brand New. Nº de ref. de la librería 0198701306

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Descripción Oxford University Press. Hardback. Estado de conservación: new. BRAND NEW, New Foundations for Physical Geometry: The Theory of Linear Structures, Tim Maudlin, 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. Nº de ref. de la librería B9780198701309

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Descripción OUP Oxford, 2014. HRD. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería FU-9780198701309

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Descripción 2014. HRD. Estado de conservación: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Nº de ref. de la librería VU-9780198701309

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Descripción Oxford Univ Pr, 2014. Hardcover. Estado de conservación: Brand New. 352 pages. 9.50x6.50x1.00 inches. In Stock. Nº de ref. de la librería __0198701306

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Descripción Hardcover. Estado de conservación: New. Ship out 1-2 business day,Brand new,US edition, Free tracking number usually 2-4 biz days delivery to worldwide Same shipping fee with US, Canada,Europe country, Australia, item will ship out from either LA or Asia k. Nº de ref. de la librería ABE-12536323456

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