Study on some Basic Results in Real Analysis
- 주제(키워드) Riemann integral , continuous functions , real analysis
- 발행기관 서강대학교 일반대학원
- 지도교수 김현석
- 발행년도 2011
- 학위수여년월 2011. 8
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000046905
- 본문언어 영어
- 저작권 서강대학교의 논문은 저작권보호를 받습니다.
초록/요약
In this thesis, we study several classical results in real analysis. We first prove the Bolzano-Weierstrass theorem and the Heine-Borel theorem and then introduce the notion of tagged partitions. They will be used to provide different proofs of basic results for continuous functions on bounded and closed intervals in R. We also prove the Lebesgue criterion of Riemann integrable funtions by using the Heine-Borel theorem and the method of tagged partitions.
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