Re: [高微] 期中考古

看板Math作者 (臣又又-Chanyoyo)時間12年前 (2013/04/16 00:08), 編輯推噓6(6推 0噓 31→)
留言37則, 9人參與, 6年前最新討論串2/2 (看更多)
其中有一題是要證 If F is closed and K is compact ,then F 交集 K is compact. 我想要問一下 能有例子是舉出 F is closed 但不是bounded的嗎？ 不然我想在R^n空間裡好像closed必然等於會有bounded的情況出現， 那麼兩個compact set的交集必然compact了。 還有希望其他題能提點一下 QQ 非數學本系突然大三要搞這方面真是有點難 . . . -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 1.169.149.188
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04/16 00:12, , 1F
不太懂 要有個F closed but not bounded很容易
04/16 00:12, 1F
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04/16 00:12, , 2F
但是 F 交集 K 一定 bounded
04/16 00:12, 2F
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04/16 00:12, , 3F
R^n就是closed
04/16 00:12, 3F
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04/16 00:13, , 4F
{m|m是整數} 也是closed
04/16 00:13, 4F
推
04/16 00:21, , 5F
加油
04/16 00:21, 5F
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04/16 00:23, , 6F
搞不太懂 為何{m│m是整數}為closed？
04/16 00:23, 6F
推
04/16 00:27, , 7F
從定義下手吧 因為它的補集是open
04/16 00:27, 7F
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04/16 00:32, , 8F
同上 closed<=>補集open<=>包含所有limit pts
04/16 00:32, 8F
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04/16 00:33, , 9F
直觀圖形上 "要包含所有邊界"
04/16 00:33, 9F
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04/16 00:51, , 10F
因為R^N上，F is closed 和 K is compact
04/16 00:51, 10F
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04/16 00:52, , 11F
所以必集合的任意交集必為必集合，且K帶有bound性質
04/16 00:52, 11F
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04/16 00:52, , 12F
故F交集K必然為closed and bounded故可推出其compact
04/16 00:52, 12F
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04/16 00:52, , 13F
?
04/16 00:52, 13F
推
04/16 00:56, , 14F
YES
04/16 00:56, 14F
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04/16 00:56, , 15F
是
04/16 00:56, 15F
推
04/16 00:56, , 16F
隊
04/16 00:56, 16F
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04/16 00:58, , 17F
喔喔喔~~燃起一線生機...現在來看2.2..ˊ_ˋ
04/16 00:58, 17F
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04/16 01:38, , 18F
看不懂第三題問 if x/y 的意思....
04/16 01:38, 18F
推
04/16 02:06, , 19F
應該是x不等於y的符號只是這張印刷不清楚
04/16 02:06, 19F
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04/16 02:11, , 20F
恩，我寄信給老師了，看他怎樣回
04/16 02:11, 20F
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04/16 02:12, , 21F
04/16 02:12, 21F
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04/16 02:12, , 22F
直立版本的原卷，剩下2,3,6求指點 Or2
04/16 02:12, 22F
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04/16 02:29, , 23F
3 done ^_^
04/16 02:29, 23F
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04/16 11:39, , 24F
有人能教我6.2怎證嗎？寫到剩下這題了
04/16 11:39, 24F
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04/16 12:22, , 25F
取個d(y, x_n)->inf_x in C d(y, x_n),再用連續,
04/16 12:22, 25F
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04/16 12:22, , 26F
Sequentially compact
04/16 12:22, 26F
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04/16 12:26, , 27F
證 x_n 有 subsequence 收歛
04/16 12:26, 27F
推
04/17 00:29, , 28F
請問你的命題是R^N版本 還是一般metric space的命題
04/17 00:29, 28F
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04/17 00:29, , 29F
版本?
04/17 00:29, 29F
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04/17 00:37, , 30F
R^N
04/17 00:37, 30F
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08/13 17:34, , 31F
同上 closed<= https://noxiv.com
08/13 17:34, 31F
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09/17 15:27, , 32F
Sequentiall https://daxiv.com
09/17 15:27, 32F
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11/10 11:40, , 33F
//noxiv.com
11/10 11:40, 33F
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11/10 11:40, , 34F
11/10 11:40, 34F
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01/02 15:21, 7年前 , 35F
01/02 15:21, 35F
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07/07 10:53, 6年前 , 36F
//noxiv.com
07/07 10:53, 36F
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07/07 10:53, 6年前 , 37F
07/07 10:53, 37F
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