[請益] continuity
※ [本文轉錄自 Economics 看板]
作者: ninmit (silent all the years) 站內: Economics
標題: [請益] continuity
時間: Thu Nov 5 04:18:40 2009
關於連續 (continuity) , 看了很久還是不懂, 所以想請教各位先進.
在 Jehle and Reny (p.8, 2001), 定義 continuity 為
For all x belongs to R(n)+, the "at least as good as" set >= (x), and
the "no better than" set <=(x), are closed in R(n)+.
然後, 在 Varian (p.95, 1992) 定義則是
For all y in X, the sets {x:x>=y} and {x:x<=y} are closed sets.
It follows that {x:x>y} and {x:x<y} are open sets.
在 Open set 和 Closed set 方面我都懂. 我的問題是:
為什麼兩個 closed set 就會形成連續?
這是否在說明: 以 Jehle and Reny 的圖 1.2 (p.9) 來說明, 因為 x 是 better set 和
worse set 的交集, 然後 better set 和 worse set 都是 closed, 所以 x 所形成的集合
是連續??!!
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