[幾何] cantor set

看板Math作者 (cholauda)時間14年前 (2012/05/28 09:51), 編輯推噓2(2推 0噓 10→)
留言12則, 3人參與, 最新討論串1/1
請教大大 "The image of a Cantor set for a homeomorphism between topological spaces is a Cantor set." 這句話該怎麼證明？ 或者說有references可提供小弟參閱研讀？ 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.113.150.197
推
05/28 20:30, , 1F
證明他是沒有內點的完美集?
05/28 20:30, 1F
→
05/29 13:53, , 2F
哦...只有給這麼一句話...應該是這個意思吧?!
05/29 13:53, 2F
推
05/29 16:17, , 3F
Let C be a cantor set, and f be a homeo.
05/29 16:17, 3F
→
05/29 16:19, , 4F
If int(f(C)) is nonempty,
05/29 16:19, 4F
→
05/29 16:19, , 5F
suppose x is in int(f(C)) and a nhd U of x
05/29 16:19, 5F
→
05/29 16:20, , 6F
then f^{-1}(U) is a open set in C
05/29 16:20, 6F
→
05/29 16:21, , 7F
(應該是這樣吧
05/29 16:21, 7F
→
05/29 16:21, , 8F
接著就只要證明f(C)'=f(C) 應該也算簡單吧XD
05/29 16:21, 8F
→
05/29 16:22, , 9F
只是我不確定這樣是不就是Cantor set就試了
05/29 16:22, 9F
→
05/29 18:53, , 10F
謝謝大大~ 我來研讀一下~
05/29 18:53, 10F
→
08/13 16:53, , 11F
接著就只要證明f(C) https://noxiv.com
08/13 16:53, 11F
→
09/17 14:49, , 12F
謝謝大大~ 我來研讀一 https://daxiv.com
09/17 14:49, 12F
‣ 更多 cholauda 的文章
文章代碼(AID): #1Fmjeo3s (Math)