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.Supposexisintheunionof\bar{A_i}''s,thenthereexistssomek>=1sucht
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