Proof of Heine-Borel theorem(일부)
Heine-Borel theorem
Let K be the subset of R(set of real numbers)
Then the following are equivalent
(a) K is closed and bounded
(b) K is compact
(c) Every infinite subset of K has a limit point in K
proof of (c)=>(a)
(i) Claim 1: K is bounded
(ii) Claim 2: K is closed
진짜 기말 공부하면서 제일 머리 터지는 곳이 compact set인듯
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