[微積] 高微 disconnected

[dongchia (開始懂了)]

The Cantor set F is wildly disconnected.

Show that if x,y is in F,x不等於y, then there is a disconnection A,B of F,such

that x屬於A,y 屬於B.


Bartle 的題目，不知道該怎麼找open sets A, B，請問該如何定義A B?

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→ k6416337    :Cantor set是指每次都挖1/3^k長度的那個嗎?
→ d628525     :En is the union of 2^n closed subintervals of
→ d628525     :[0,1],each of length 3^-n,the total length of En
→ d628525     :is (2/3)^n,the set P=En交集從n=1~無限,it is
→ d628525     :called Cantor set
→ cgkm        :x and y must lie in two distinct (and disjoint)
→ cgkm        :closed subintervals for some n