02959nam a22004458i 4500001001500000003000700015005001700022006001900039007001500058008004100073020002600114020003000140035003700170040002900207050002300236082001400259099002000273100003500293245008000328246005400408264005200462300005900514336002600573337002600599338003600625490005800661500007300719520114300792650002301935650002901958730002901987776003502016830005902051856009202110907003202202998004402234999008202278952006102360856009202421mig00005065256UkCbUP20151005020621.0m|||||o||d||||||||cr||||||||||||100303s1979||||enk o ||1 0|eng|d a9780511721533 (ebook) z9780521228459 (paperback)00aocm00000001camebacr9780511721533 aUkCbUPbengerdacUkCbUP00aQA251.3b.B78 197900a512.4219 aElectronic book1 aBrumfiel, Gregory W.,eauthor.10aPartially ordered rings and semi-algebraic geometry /cGregory W. Brumfiel.3 aPartially Ordered Rings & Semi-Algebraic Geometry 1aCambridge :bCambridge University Press,c1979. a1 online resource (280 pages) :bdigital, PDF file(s). atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier1 aLondon Mathematical Society lecture note series ;v37 aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). aThe 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. 0aCommutative rings. 0aCategories (Mathematics)0 aCambridge EBA Collection08iPrint version: z9780521228459 0aLondon Mathematical Society lecture note series ;v37.40uhttps://ezproxy.mtsu.edu/login?url=https://doi.org/10.1017/CBO9780511721533zCONNECTt0 a3903971b08-25-20c03-18-19 awib08-25-20cmdz e-fenggenkh0i2ffi1480a83f-1041-4ec5-afb2-810fdd86572esf3b2f143-ffe8-4340-9d4e-20d816224486t0fft1eQA251.3 .B78 1979hLibrary of Congress classification40t0uhttps://ezproxy.mtsu.edu/login?url=https://doi.org/10.1017/CBO9780511721533zCONNECT