[转载] Re: 问点问题# Economics - 经济
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【 以下文字转载自 PKU 讨论区 】
【 原文由 zhyue 所发表 】
3.since every element of K is isolated, then for each element k of K
we can find r(k) s.t. intersection of open ball Br(k) and K is {k}.
Then all these open balls forms an open cover of K. suppose K is not
finite, then this open cover has no finite subcover, contradict with
K is compact. QED
2.a) is easy.
b) suppose inf(p*B1)+...+inf(p*Bm) is not inf(p*B), i.e there exists
b of B, s.t. p*b
【 原文由 zhyue 所发表 】
3.since every element of K is isolated, then for each element k of K
we can find r(k) s.t. intersection of open ball Br(k) and K is {k}.
Then all these open balls forms an open cover of K. suppose K is not
finite, then this open cover has no finite subcover, contradict with
K is compact. QED
2.a) is easy.
b) suppose inf(p*B1)+...+inf(p*Bm) is not inf(p*B), i.e there exists
b of B, s.t. p*b