[微積] Continuous function

看板Math作者 (臣又又-Chanyoyo)時間12年前 (2013/03/28 00:23), 編輯推噓1(1推 0噓 5→)
留言6則, 4人參與, 最新討論串1/1
Suppose f: R^n -> R is a continuous function . Show that the set [x屬於R^n的元素│f(x)=0] is a closed set. 求提點 @@ -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 1.169.128.156
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03/28 00:41, , 1F
法一:證明{x|f(x)>0},{x|f(x)<0} are open
03/28 00:41, 1F
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03/28 00:42, , 2F
法二：S is closed <=> S的closure = S來證
03/28 00:42, 2F
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03/28 00:42, , 3F
主要用連續性的定義或性質就能簡單證明出來了
03/28 00:42, 3F
推
03/28 00:52, , 4F
在你那個集合挑一個收斂點列收斂到x*，去證明f(x*)=0
03/28 00:52, 4F
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03/28 11:14, , 5F
連續函數把closed set拉回closed set
03/28 11:14, 5F
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03/28 11:31, , 6F
謝謝喔 會証了^_^
03/28 11:31, 6F
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