Partially Ordered Rings and Semi-Algebraic Geometry Gregory W. Brumfiel

ISBN: 9780521228459

Published: November 30th 2007

Paperback

292 pages


Description

Partially Ordered Rings and Semi-Algebraic Geometry  by  Gregory W. Brumfiel

Partially Ordered Rings and Semi-Algebraic Geometry by Gregory W. Brumfiel
November 30th 2007 | Paperback | PDF, EPUB, FB2, DjVu, audiobook, mp3, ZIP | 292 pages | ISBN: 9780521228459 | 3.67 Mb

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 andMoreThe 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 Brumfiels 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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