※ 引述《iamagine (A-gine)》之銘言：
: Check whether the set E = {(x,y)| x E [0,1] , and y = 1 if x is rational
: y = 0 if x is irrational} in |R^2 is compact or not. If E is not compact ,
: find the smallest compact set K such that EㄈK. Justify your answer.
: 麻煩大大們了>""<
從 Heine-Borel 定理 , E 是 compact <=> E is closed & bounded
當然 E 是 bounded 但不是 closed , 所以 E 並不是 compact .
K 是包含 E 的最小的 closed & bounded 的集合
因此 K = closure of E
希望是對的 , 有錯請指教
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