Macroeconomics Exam Review 91

Macroeconomics Exam Review 91 - ( x ) for every x , we must...

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Unformatted text preview: ( x ) for every x , we must have ( x ) = x . Therefore, ( x ) = x which implies that ( x ) = x . That is, x is a fixed point of . Brouwer = no-retraction Exercise 2.132. 2.135 Let , = 1 , 2 ,... be a sequence of simplicial partitions of in which the maximum diameter of the subsimplices tend to zero as . By Sperners lemma (Proposition 1.3), every partition has a completely labeled subsimplex with vertices x , x 1 ,..., x . By construction of an admissible labeling, each x belongs to a face containing x , that is x conv { x ,... } and therefore x , = 0 , 1 ,..., Since is compact, each sequence x has a convergent subsequence x . Moreover, since the diameters of the subsimplices converge to zero, these subsequences must converge to the same point, say...
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.

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