View in EDS PDF Full Text ePub Full Text

New Foundations for Physical Geometry : The Theory of Linear Structures

Saved in:
Bibliographic Details
Title: New Foundations for Physical Geometry : The Theory of Linear Structures
Description: 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.
Authors: Tim Maudlin
Resource Type: eBook.
Subjects: Geometry--Philosophy, Algebras, Linear, Space and time--Mathematics, Raumstruktur, Topologischer Raum, Raum-Zeit
Categories: PHILOSOPHY / General
Database: eBook Collection (EBSCOhost)
FullText Links:
  – Type: ebook-pdf
  – Type: ebook-epub
Text:
  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 707100
RelevancyScore: 1057
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1057.36352539063
IllustrationInfo
ImageInfo – Size: thumb
  Target: https://rps2images.ebscohost.com/rpsweb/othumb?id=NL$707100$PDF&s=r
– Size: medium
  Target: https://rps2images.ebscohost.com/rpsweb/othumb?id=NL$707100$PDF&s=d
Items – Name: Title
  Label: Title
  Group: Ti
  Data: New Foundations for Physical Geometry : The Theory of Linear Structures
– Name: Abstract
  Label: Description
  Group: Ab
  Data: 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.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Tim+Maudlin%22">Tim Maudlin</searchLink>
– Name: TypePub
  Label: Resource Type
  Group: TypPub
  Data: eBook.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Geometry--Philosophy%22">Geometry--Philosophy</searchLink><br /><searchLink fieldCode="DE" term="%22Algebras%2C+Linear%22">Algebras, Linear</searchLink><br /><searchLink fieldCode="DE" term="%22Space+and+time--Mathematics%22">Space and time--Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Raumstruktur%22">Raumstruktur</searchLink><br /><searchLink fieldCode="DE" term="%22Topologischer+Raum%22">Topologischer Raum</searchLink><br /><searchLink fieldCode="DE" term="%22Raum-Zeit%22">Raum-Zeit</searchLink>
– Name: SubjectBISAC
  Label: Categories
  Group: Su
  Data: <searchLink fieldCode="ZK" term="%22PHILOSOPHY+%2F+General%22">PHILOSOPHY / General</searchLink>
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=707100
RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 514.223
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Geometry--Philosophy
        Type: general
      – SubjectFull: Algebras, Linear
        Type: general
      – SubjectFull: Space and time--Mathematics
        Type: general
      – SubjectFull: Raumstruktur
        Type: general
      – SubjectFull: Topologischer Raum
        Type: general
      – SubjectFull: Raum-Zeit
        Type: general
    Titles:
      – TitleFull: New Foundations for Physical Geometry : The Theory of Linear Structures
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Tim Maudlin
      – PersonEntity:
          Name:
            NameFull: Tim Maudlin
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2014
            – D: 14
              M: 03
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9780198701309
            – Type: isbn-print
              Value: 9780191022692
            – Type: isbn-electronic
              Value: 9780191004551
          Titles:
            – TitleFull: New Foundations for Physical Geometry : The Theory of Linear Structures
              Type: main
ResultId 1