Partially Ordered Rings and Semi-algebraic Geometry

Partially Ordered Rings and Semi-algebraic Geometry

eBook - 1979
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Cambridge Univ Pr
The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology.
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.

Publisher: Cambridge [England] ; New York : Cambridge University Press, 1979
ISBN: 9780511891922
051189192X
9781107360921
1107360927
9780521228459
052122845X
Characteristics: 1 online resource (280 pages) : illustrations

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