By Veblen O., Whitehead J. H.
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The good paintings that based analytical geometry. incorporated this is the unique French textual content, Descartes’ personal diagrams, including the definitive Smith-Latham translation. "The maximum unmarried step ever made within the growth of the precise sciences. "— John Stuart Mill.
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5 (i) tells us that the diagram 41 l@s" (1) s@l C, _8 h*(Y)< h C, _8 D, h EI(X . @ Y; ~*)< is commutative, >h EI(X , 8 Y,;~*) where the columns are the E these are isomorphlsms of chain complexes, resolutions. (X) 9 h D, > E I ( X @ Y,; ~*) pairings ~ of spectral sequences. , as X, and Y, are both Hence they induce isomorphlsms of homology. Now 1 @ ~" , ~ | 1 also induce isomorphisms of homology - this is part of the basic definition of Tor, , see and the pth homology greup of each complex in the top row of (1) is canonically identified with Tor~P(~*(X), ~*(Y)).
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