[高微] A,B closed 判斷A+B是否closed
題目是: Let A,B ≦ R^n be closed set.
Does A+B = {x+y | x€A and y€B} have to be closed?
解答是找例子 A={(x,0) €R^2 | x€R}
B={(t,1/t) €R^2 | t>0}
我自己是從定義著手
A is closed => (R^n - A) is open
B is closed => (R^n - B) is open
to defined whether A+B is closed or not,we consider R^n-(A+B)
R^n-(A+B) = R^n-A-B = (R^n-A)-B
since R^n-A is open , and B is close
=> R^n-(A+B) is not open
Hence A+B is not closed ##
問題點就是說 open - closed = closed 能不能推過去..
感覺這個也是要舉例證明.....囧
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 114.42.103.126
→
12/13 17:03, , 1F
12/13 17:03, 1F
推
12/13 17:44, , 2F
12/13 17:44, 2F
→
12/13 17:44, , 3F
12/13 17:44, 3F
→
12/13 17:51, , 4F
12/13 17:51, 4F
→
12/13 19:48, , 5F
12/13 19:48, 5F
→
12/13 20:33, , 6F
12/13 20:33, 6F
→
12/13 23:40, , 7F
12/13 23:40, 7F
→
12/14 10:12, , 8F
12/14 10:12, 8F
→
12/14 10:14, , 9F
12/14 10:14, 9F
→
12/15 00:12, , 10F
12/15 00:12, 10F
→
12/15 00:13, , 11F
12/15 00:13, 11F
→
12/15 00:14, , 12F
12/15 00:14, 12F
→
12/15 00:15, , 13F
12/15 00:15, 13F
推
12/15 01:26, , 14F
12/15 01:26, 14F
→
12/15 01:27, , 15F
12/15 01:27, 15F
討論串 (同標題文章)
以下文章回應了本文 (最舊先)：
完整討論串 (本文為第 1 之 4 篇)：