Partially ordered rings and semialgebraic geometry /
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...
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Format:  eBook 
Language:  English 
Published: 
Cambridge :
Cambridge University Press,
1979.

Series:  London Mathematical Society lecture note series ;
37. 
Subjects:  
Online Access:  CONNECT CONNECT 
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050  0  0  a QA251.3 b .B78 1979 
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100  1  a Brumfiel, Gregory W., e author.  
245  1  0  a Partially ordered rings and semialgebraic geometry / c Gregory W. Brumfiel. 
246  3  a Partially Ordered Rings & SemiAlgebraic Geometry  
264  1  a Cambridge : b Cambridge University Press, c 1979.  
300  a 1 online resource (280 pages) : b digital, PDF file(s).  
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490  1  a London Mathematical Society lecture note series ; v 37  
500  a Title from publisher's bibliographic system (viewed on 05 Oct 2015).  
520  a 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.  
650  0  a Commutative rings.  
650  0  a Categories (Mathematics)  
730  0  a Cambridge EBA Collection  
776  0  8  i Print version: z 9780521228459 
830  0  a London Mathematical Society lecture note series ; v 37.  
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