By Bocconi

Notes for Bocconi utilized Math critical half summarizing lecture notes and routines.

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Additional resources for Applied math. Part 1: Integral

Sample text

J E I } covers (0,11 and a b E [0,11 we have a E U3 for for is open there is an open interval (a-e,a+e) c a positive integer N so that 2 and hence bN - aN (c. However a E [aN,bN] and a - aN 0. Since Choose The above argument could be extended to show that the unit n-cube . 8 Theorem on. Let f: X -' Y be a continuous map. If S c X is a compact subspace, then f(S) is compact.

If X is a topological space upon which G acts then we can give X/G the quotient topology. We call X/G with the quotient topology the quotient space of X by G. For example if Z 2 acts on Sn by ±1x = ix then is just + x then R/Z just S'. 9 Exercises (a) Let Xbe the infinite strip {(x,y)E R2;-½

Let b be the greatest lower bound of the set { b1 ,b2 ,... } By definition we - - wehaveb- a< for each n and so a = b. Since f El. j E I } covers (0,11 and a b E [0,11 we have a E U3 for for is open there is an open interval (a-e,a+e) c a positive integer N so that 2 and hence bN - aN (c. However a E [aN,bN] and a - aN 0. Since Choose The above argument could be extended to show that the unit n-cube .