해석학 정리본

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"해석학 정리본"에 대한 내용입니다.

목차

01: Extend of Q (유리수의 확장)
02: Topology (기초 위상 수학)
03: Sequence and Series (수열과 급수)
04: Special sequence and series (특수한 수열과 급수)
05: Specific Algebraic Structure and Space (특수한 대수 구조와 공간)
06: Continuity of the function (함수의 연속성)
07: Operation of the functions (함수의 연산자)
08: Sequences and Series of function (함수의 수열, 급수)
09: Fourier Approximation (푸리에 근사)

본문내용

Ordered Sets
Def:Ordered set
Ordered set (S,<) is a set with a relation<defined on S such that,
(i)∀x,y∈S, the one and only one of next three statementsare true:
x < y,x=y,y < x
(ii)∀x,y,z∈S, if x < y and y < z then x < z (transitivity)

Def:Upper/Lower bound of subset E
For ordered set (S,<) and its subsetE∈S, we call it is bounded above/below if
∃α ∈ S α≥x/α≤x ∀x ∈ E
Such α is called an upper/lower bound of E.
Def: Supremum & Infimum
For upper/lower bound α of subset E, it is called supremum/infimum of E. if it satisfies following properties.

참고 자료

Rudin, Principles of Mathematical Analysis, 3rd edition, (McGraw-Hill, 1976), ISBN: 0070856133