Partially ordered rings and semi-algebraic geometry
WORLDSHARE SUB RECORDS
Brumfiel, Gregory W.
creator
text
bibliography
enk
Cambridge [England]
New York
Cambridge University Press
1979
monographic
eng
1 online resource (280 pages) : illustrations.
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.
Gregory W. Brumfiel.
Includes bibliographical references (pages 273-277) and index.
Commutative rings
Categories (Mathematics)
QA251.3 .B78 1979eb
512.4
31.51
31.61
SI 320
SK 240
31.11
Partially ordered rings and semi-algebraic geometry
Brumfiel, Gregory W.
Cambridge [Eng.] ; New York : Cambridge University Press, 1979
(DLC) 80469087
(OCoLC)6022756
London Mathematical Society lecture note series ; 37
9781107360921
1107360927
9780511891922
051189192X
052122845X
9780521228459
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130415
20210517060130.5
mig00005328086
eng