作者weibo (打混鬼)
看板Math
標題[分析] 證明子集交集為零 in Metric Space
時間Thu Oct 22 13:40:50 2009
Q: (X,d) be a metric space. Prove that F1 and F2 are two disjoint
closed sets in X, then exists two open sets in X, O1)F1, and O2)F2,
such taht O1 interaction O2 = empty
請大家幫幫忙了!!我想了好久都不知道怎麼下筆阿!!
謝謝囉!!
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推 HmmHmm :hint: 用F1 跟 F2 的 distance 10/22 14:08
推 math1209 :除了樓上的方法外, 反證也行. 10/22 14:12
推 FANggot :Construct a open cover with open neighboorhoods 10/22 14:34