[分析] compact
想請問有關compact的定義
rudin上面寫的
the requirement is that if {Ga} is an open cover of K, then
there are finitely many indices a1,a2.....an such that
K屬於Ga1聯集Ga2聯集... Gan
可是照這樣看的話 我只要找到ㄧ個open cover去蓋K
然後a1,a2...an不是有限項 我就可以說這個K不是compact?
以R中[0,1]為例 這應該是compact
那我對此範圍內的所有實數都取開區間(r-n,r+n) n為任意數
這樣不管我區間的寬度怎選 我都可以找到無窮的開區間去蓋[0,1]阿
感覺也符合rudin的定義
想請高手幫幫忙
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