作者steve1012 (steve)
看板Math
標題[微積] Interior, boundary of a set
時間Sat May 14 17:45:26 2011
Let S= {x1,x2 ... xn} be a nonempty, finite set of points.
(A)what is the interior of S?
(B)Waht is the boundary of S?
(C) Is S open , closed or neither?
答案A是 空集合
(B) S本身
(C) Closed set
這邊我有點不懂
是因為S是離散的點組成的所以interior是空集合嗎？
要怎麼用定義去理解
另外我想問問這塊地方跟後面的微積分有什麼關係呢
一直不太懂
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1F：→ thisday :你用的課本是? 05/14 17:54
2F：→ wickeday :不用想太多，就直接用定義去做就好了… 05/14 18:16
3F：→ steve1012 :我用的課本是Salas 可是定義我不知道怎麼搞 05/14 18:25
4F：→ steve1012 :之前去翻C&J還有幾本高微也有在講集合的部分 05/14 18:25
5F：→ steve1012 :搞不太懂這部份與後面微積分的關係 05/14 18:25
6F：→ THEJOY :引入點集拓樸來敘述δ-ε語言 05/14 18:50
7F：→ h2o1125 :if x is an interior of S, any neighboorhood of x 05/14 20:13
8F：→ h2o1125 :will contain infinte point of S, but S is finte 05/14 20:14
9F：→ h2o1125 :so the interior of S is empty 05/14 20:15
10F：→ h2o1125 :any small enough neighboorhood of x 才對 05/14 20:15
11F：→ h2o1125 :不對 我在搞笑不好意思 這應該是錯的 05/14 20:16
12F：→ h2o1125 :if x is an interior of S, x must be xn for some n 05/14 20:20
13F：→ h2o1125 :since any neighboorhood of x isn't contained in S 05/14 20:22
14F：→ h2o1125 :hence there are no neighboorhood of x such that 05/14 20:24
15F：→ h2o1125 :the neighboorhood of x is contained in S 05/14 20:25
16F：→ h2o1125 :the interior is empty 05/14 20:25
17F：→ h2o1125 :the boundary of S is S unioning the limit point 05/14 20:28
18F：→ h2o1125 :of S, and the limit point of S is empty 05/14 20:29
19F：→ h2o1125 :if x is an limitpoint of S,any neighboorhood of x 05/14 20:30
20F：→ h2o1125 :will contain infinte point of S, but S is finte 05/14 20:31
21F：→ h2o1125 :so the limit point set of S is empty 05/14 20:31
22F：→ h2o1125 :hence the boundary of S is S 05/14 20:31
23F：→ h2o1125 :上面又不對了 又搞笑了 05/14 20:32
24F：→ steve1012 :拜託大大根我解釋了 還是我該去番什麼書有詳細講 05/14 22:45
25F：→ ricestone :你先把定義寫出來再去考慮如何套 05/14 22:46
26F：→ steve1012 :A point Xo is said to be an interior of the 05/14 23:38
27F：→ steve1012 :set S if Scontains some neighborhood of Xo 05/14 23:39
28F：→ steve1012 :要怎麼用 05/14 23:39
29F：→ ricestone :所以各點[x1,x2,x3...]之間都有距離 05/14 23:46
30F：→ ricestone :取這些可能的距離裡面最小的距離為r 05/14 23:46
31F：→ ricestone :則對任何一點來說，它的距離r以內的鄰域(neighboor) 05/14 23:48
32F：→ ricestone :都不包含任何一個S集合內的點 05/14 23:50
33F：→ ricestone :反過來說就是任何一個xn的鄰域都沒被S包住 05/14 23:52
34F：→ ricestone :所以每一個xn都不是S的interior，所以S沒有interior 05/14 23:53