推 iamagine:謝謝大大解惑>////< 終於了解嚕 07/18 19:33
※ 引述《iamagine (A-gine)》之銘言：
: Let E is open in |R^(n+p).
: Let W = {t€|R^p | (0,t) € E } 其中 0 € |R^n
: 問題： W is open in |R^p ??
(0,t) € E => 存在open ball B with center (0,t) such that B < E
Let Bp = {t€|R^p | (0,t) € B }
then Bp is an open ball with center t in |R^p,
and Bp € W => W is open
: Let E is a subset in |R^(n+p).
: Let W = {t€|R^p | (0,t) € E } 其中 0 € |R^n
: If W is open in |R^p
: 問題： E is open in |R^(n+p) ??
p=n=1
E = [0,1] X (0,1)
then W = (0,1) is open in |R
but E is not open in |R^2
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★silvermare,我想問妳,妳死後願不願意葬在我家的祖墳?
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