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  3. Partially Ordered Rings and Semi-Algebraic Geometry
  • Cited by 55
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2010
      December 1979
      ISBN:
      9780511721533
      9780521228459
      DOI:
      https://doi.org/10.1017/CBO9780511721533
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.4kg, 292 Pages
      • Subjects:
      Mathematics (general), Mathematics, Geometry and Topology
      Series:
      London Mathematical Society Lecture Note Series (37)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (37)
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    Book description

    The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance.

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