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標題: metric [打印本頁]

作者: kwoklap 時間: 11-2-13 05:42 AM 標題: metric

Prove that any subset in a finite metric space is open

help thx

作者: Naozumi 時間: 11-2-14 12:03 AM

如果學左任何finite set都係 closed set就唔洗點做啦

未學咪define個 d = max{xi, xj} , finite set個min實存在,根本你再諗下

作者: kwoklap 時間: 11-2-14 04:27 PM

我其實有一個idea係take ε = min(d(x,y)), where x=/=y , for all x, y in the finite set
then for all z in the subset U, B(z,ε) = {z} which is in U
therefore U is open

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