作业帮数分原理第二章第七题求证
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数分原理第二章第七题求证
数分原理第二章第七题
求证
数分原理第二章第七题求证
b.Suppose x is in the union of \bar{A_i}'s,then there exists some k>=1 such that x is in \bar{A_k}.Hence,there is a sequence {x_1,x_2,..} in A_k with limit point x.Notice that each x_j (j>=1) is in A_k,and so is in B--the union of all A_i's.This gives us a sequence {x_1,x_2,..} in B with limit point x,which implies x is in \bar{B}.
a.Using the same argument as above we can show the right is contained in left (k now satisfies 1