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New foundations for physical geometry : the theory of linear structures /
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original theory of linear struct...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Oxford University Press,
2014.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | EBSCO_ocn872566569 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
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| 008 | 140313s2014 enka ob 001 0 eng d | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Maudlin, Tim, |e author. | |
| 245 | 1 | 0 | |a New foundations for physical geometry : |b the theory of linear structures / |c Tim Maudlin. |
| 264 | 1 | |a Oxford : |b Oxford University Press, |c 2014. | |
| 300 | |a 1 online resource (ix, 363 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 588 | 0 | |a Online resource; title from pdf information screen (Ebsco, viewed March 12, 2014). | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | 8 | |a Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original theory of linear structures. | |
| 505 | 0 | 0 | |g Machine generated contents note: |t Metaphorical and Geometrical Spaces -- |t A Light Dance on the Dust of the Ages -- |t The Proliferation of Numbers -- |t Descartes and Coordinate Geometry -- |t John Wallis and the Number Line -- |t Dedekind and the Construction of Irrational Numbers -- |t Overview and Terminological Conventions -- |g 1. |t Topology and Its Shortcomings -- |t Standard Topology -- |t Closed Sets, Neighborhoods, Boundary Points, and Connected Spaces -- |t The Hausdorff Property -- |t Why Discrete Spaces Matter -- |t The Relational Nature of Open Sets -- |t The Bill of Indictment (So Far) -- |g 2. |t Linear Structures, Neighborhoods, Open Sets -- |t Methodological Morals -- |t The Essence of the Line -- |t The (First) Theory of Linear Structures -- |t Proto-Linear Structures -- |t Discrete Spaces, Mr Bush's Wild Line, the Woven Plane, and the Affine Plane -- |t A Taxonomy of Linear Structures -- |t Neighborhoods in a Linear Structure -- |t Open Sets. |
| 505 | 0 | 0 | |t Finite-Point Spaces -- |t Return to Intuition -- |t Directed Linear Structures -- |t Linear Structures and Directed Linear Structures -- |t Neighborhoods, Open Sets, and Topologies Again -- |t Finite-Point Spaces and Geometrical Interpretability -- |t A Geometrically Uninterpretable Topological Space -- |t Segment-Spliced Linear Structures -- |t Looking Ahead -- |t Exercises -- |t Appendix: Neighborhoods and Linear Structures -- |g 3. |t Closed Sets, Open Sets (Again), Connected Spaces -- |t Closed Sets: Preliminary Observations -- |t Open and Closed Intervals -- |t JP-closed and JP-open Sets -- |t Jp-open Sets and Open Sets, JP-closed Sets and Closed Sets -- |t Zeno's Combs -- |t Closed Sets, Open Sets, and Complements -- |t Interiors, Boundary Points, and Boundaries -- |t Formal Properties of Boundary Points -- |t Connected Spaces -- |t Chains and Connectedness -- |t Directedness and Connectedness -- |t Exercises -- |g 4. |t Separation Properties, Convergence, and Extensions -- |t Separation Properties -- |t Convergence and Unpleasantness. |
| 505 | 0 | 0 | |t Sequences and Convergence -- |t Extensions -- |t The Topologist's Sine Curve -- |t Physical Interlude: Thomson's Lamp -- |t Exercises -- |g 5. |t Properties of Functions -- |t Continuity: an Overview -- |t The Intuitive Explication of Continuity and Its Shortcomings -- |t The Standard Definition and Its Shortcomings -- |t What the Standard Definition of Continuity Defines -- |t The Essence of Continuity -- |t Continuity at a Point and in a Direction -- |t An Historical Interlude -- |t Remarks on the Architecture of Definitions; Lineal Functions -- |t Lines and Continuity in Standard Topology -- |t Exercises -- |g 6. |t Subspaces and Substructures; Straightness and Differentiability -- |t The Geometrical Structure of a Subspace: Desiderata -- |t Subspaces in Standard Topology -- |t Subspaces in the Theory of Linear Structures -- |t Substructures -- |t One Way Forward -- |t Euclid's Postulates and the Nature of Straightness -- |t Convex Affine Spaces -- |t Example: Some Conical Spaces -- |t Tangents -- |t Upper and Lower Tangents, Differentiability -- |t Summation -- |t Exercises. |
| 505 | 0 | 0 | |g 7. |t Metrical Structure -- |t Approaches to Metrical Structure -- |t Ratios Between What? -- |t The Additive Properties of Straight Lines -- |t Congruence and Comparability -- |t Eudoxan and Anthyphairetic Ratios -- |t The Compass -- |t Metric Linear Structures and Metric Functions -- |t Open Lines, Curved Lines, and Rectification -- |t Continuity of the Metric -- |t Exercises -- |t Appendix: A Remark about Minimal Regular Metric Spaces -- |g 8. |t Product Spaces and Fiber Bundles -- |t New Spaces from Old -- |t Constructing Product Linear Structures -- |t Examples of Product Linear Structures -- |t Neighborhoods and Open Sets in Product Linear Structures -- |t Fiber Bundles -- |t Sections -- |t Additional Structure -- |t Exercises -- |g 9. |t Beyond Continua -- |t How Can Continua and Non-Continua Approximate Each Other? -- |t Continuous Functions -- |t Homotopy -- |t Compactness -- |t Summary of Mathematical Results and Some Open Questions -- |t Exercises. |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Line geometry. | |
| 650 | 0 | |a Space and time. | |
| 650 | 6 | |a Géométrie de la ligne. | |
| 650 | 7 | |a MATHEMATICS |x Topology. |2 bisacsh | |
| 650 | 7 | |a Line geometry |2 fast | |
| 650 | 7 | |a Space and time |2 fast | |
| 650 | 7 | |a Raumstruktur |2 gnd | |
| 650 | 7 | |a Topologischer Raum |2 gnd | |
| 650 | 7 | |a Raum-Zeit |2 gnd | |
| 776 | 0 | 8 | |i Print version: |a Maudlin, Tim. |t New foundations for physical geometry : the theory of linear structures. |d Oxford, [England] ; New York, New York : Oxford University Press, ©2014 |h ix, 363 pages |z 9780198701309 |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=707100 |z Texto completo |
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