Partially Ordered Rings and Semi-Algebraic Geometry (London Mathematical Society Lecture Note Series, Series Number 37) - Softcover

Brumfiel, Gregory W.

Softcover

ISBN 10: 052122845X ISBN 13: 9780521228459

Publisher: Cambridge University Press, 1980

Synopsis

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.

About this title

Book Description

The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1980
• ISBN 10: 052122845X
• ISBN 13: 9780521228459
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 292