[分析] Cardinality、Compact
1. Let A be the set of all functions from (0,1) to |R,and
B be the set of all continuous funtions from (0,1) to |R.
(a) Show that there is no 1-1 correspondence between |R and A.
That is,|R and A do not have the same cardinlity.
(b)Prove or disprove that there is a 1-1 correspondence between |R and B.
2.Let W be a compact subset of |R^n and {Va} be an open cover of W.
Prove that there is an ε>0 such that for each subset E of W having
diameter less than ε, there si a V in {Va} containing E.
a0
1.(a)在拓樸課本的習題有看過 說＃（A）＝ 2^（c） , c是|R的個數.
可是仍不知道怎麼證明，其他題則是無頭緒，希望版上得高手能給的指教
小弟感謝萬分！
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